Originally posted by inertia
View Post
Announcement
Collapse
Message to all users:
https://carm.org/forumrules
Super Member Subscription
https://carm.org/carmsupermembersbanneradsignup
As most of you are aware, we had a crash to forums and were down for over two days a while back. We did have to do an upgrade to the vbulletin software to fix the forums and that has created changes, VB no longer provide the hybrid or threaded forums. There are some issues/changes to the forums we are not able to fix or change. Also note the link address change, please let friends and posters know of the changed link to the forums. For now this is the only link available, https://forums.carm.org/vb5/ but if clicking on forum on carm.org homepage it will now send you to this link. (edited to add https: now working.
Again, we are working through some of the posting and viewing issues to learn how to post with the changes, you will have to check and test the different features, icons that have changed. You may also want to go to profile settings,since many of the notifications, information in profile, also to update/edit your avatar by clicking on avatar space, pull down arrow next to login for user settings.
Edit to add "How to read forums, to make it easier."
Pull down arrow next to login name upper right select profile, or user settings when page opens to profile,select link in tab that says Account. Then select/choose options, go down to Conversation Detail Options, Select Display mode Posts, NOT Activity, that selection of Posts will make the pages of discussions go to last post on last page rather than out of order that happens if you choose activity threads. Then be sure to go to bottom and select SAVE Changes in your profile options. You can then follow discussions by going through the pages, to the last page having latest responses. Then click on the other links Privacy, Notifications, to select viewing options,the forums get easier if you open all the tabs or links in your profile, user settings and select options. To join Super Member, pull down arrow next to login name, select User Settings and then click on tab/link at top that says Subscriptions.
Thank you for your patience and God Bless.
Diane S
https://carm.org/forumrules
Super Member Subscription
https://carm.org/carmsupermembersbanneradsignup
As most of you are aware, we had a crash to forums and were down for over two days a while back. We did have to do an upgrade to the vbulletin software to fix the forums and that has created changes, VB no longer provide the hybrid or threaded forums. There are some issues/changes to the forums we are not able to fix or change. Also note the link address change, please let friends and posters know of the changed link to the forums. For now this is the only link available, https://forums.carm.org/vb5/ but if clicking on forum on carm.org homepage it will now send you to this link. (edited to add https: now working.
Again, we are working through some of the posting and viewing issues to learn how to post with the changes, you will have to check and test the different features, icons that have changed. You may also want to go to profile settings,since many of the notifications, information in profile, also to update/edit your avatar by clicking on avatar space, pull down arrow next to login for user settings.
Edit to add "How to read forums, to make it easier."
Pull down arrow next to login name upper right select profile, or user settings when page opens to profile,select link in tab that says Account. Then select/choose options, go down to Conversation Detail Options, Select Display mode Posts, NOT Activity, that selection of Posts will make the pages of discussions go to last post on last page rather than out of order that happens if you choose activity threads. Then be sure to go to bottom and select SAVE Changes in your profile options. You can then follow discussions by going through the pages, to the last page having latest responses. Then click on the other links Privacy, Notifications, to select viewing options,the forums get easier if you open all the tabs or links in your profile, user settings and select options. To join Super Member, pull down arrow next to login name, select User Settings and then click on tab/link at top that says Subscriptions.
Thank you for your patience and God Bless.
Diane S
https://carm.org/forumrules
See more
See less
BEAUTIFUL  Beautiful patterns in Math
Collapse
X

Originally posted by cisco qid View Post
I would sure like to look at it in your book. But unfortunately the link that you gave me only directs me to where I might purchase the book.
Comment

Originally posted by cisco qid View Post
I would sure like to look at it in your book. But unfortunately the link that you gave me only directs me to where I might purchase the book.
"The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
Comment

Originally posted by Pragmatic View Post
When I examine graphs that contain a series like (1/x^{n} + 1/x^{n+1}...) if the n is odd then the graph indicates that y = 1 when x = 1. If n is even then y = 0 when x = 1. While I am unsure how to prove this, the trend I see indicates that if (x + x^{2}...) = 0 then you would be left with (1) + 1 + (0) = 0. I am no mathematician so I am ready to be corrected on this.
For the series in question ...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0 , it states that any xvalue you choose will always sum to zero. If it is correct, then any x you choose should always provide a y =0, always.
A "p series test" helps for part of the series*.
For the form: ...+ 1/x^{p }+ 1/x^{p} + 1/x +1 ..., it will always converge if p > 1 and will diverge if p is less than or equal to 1. The pterm for 1/x is 1.
Cisco qid's correct assessment of a power series like: 1 + x + x^{2} + x^{3} +..., is useful where rules for domain provide boundary conditions.
Example: 1/(1x) = 1 + x + x^{2} + x^{3} +..., with a domain of (1 < x < 1) works.
However, for the series in question neither of these approaches is adequate to analyze its behavior. Your result using n is odd or even is interesting, but I believe that it does not provide enough information. Maybe I will try a graphical approach too.
* See: https://math.oregonstate.edu/home/pr.../pseries.html
Last edited by inertia; 013018, 03:13 PM."The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
Comment

Originally posted by inertia View Post
Interesting
For the series in question ...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0 , it states that any xvalue you choose will always sum to zero. If it is correct, then any x you choose should always provide a y =0, always.
A "p series test" helps for part of the series*.
For the form: ...+ 1/x^{p }+ 1/x^{p} + 1/x +1 ..., it will always converge if p > 1 and will diverge if p is less than or equal to 1. The pterm for 1/x is 1.
Cisco qid's correct assessment of a power series like: 1 + x + x^{2} + x^{3} +..., is useful where rules for domain provide boundary conditions.
Example: 1/(1x) = 1 + x + x^{2} + x^{3} +..., with a domain of (1 < x < 1) works.
However, for the series in question neither of these approaches is adequate to analyze its behavior. Your result using n is odd or even is interesting, but I believe that it does not provide enough information. Maybe I will try a graphical approach too.
* See: https://math.oregonstate.edu/home/pr.../pseries.html
...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0, as follows:
Start with the expression:
S = 1/x + 1/x^{2} + 1/x^{3} …
Then
S = 1/x(1 + 1/x + 1/x^{2} + …) = 1/x(1 + S) = 1/x + S/x
or
S  S/x = 1/x => S = 1/(x – 1) = 1/(1x) =  (1 + x + x^{2} + x^{3} ....) = 1/x + 1/x^{2} + 1/x^{3} …
And we get out result which we know is false since,
1/x + 1/x^{2} + 1/x^{3} … = 1/(x – 1) can't be true because x = 0 is not allowed on the LHS while it is allowed on the RHS.
 1 like
Comment

Originally posted by cisco qid View Post
Not to beat a dead horse to death but if you want to see something really weird  you can actually derive the expression,
...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0, as follows:
Start with the expression:
S = 1/x + 1/x^{2} + 1/x^{3} …
Then
S = 1/x(1 + 1/x + 1/x^{2} + …) = 1/x(1 + S) = 1/x + S/x
or
S  S/x = 1/x => S = 1/(x – 1) = 1/(1x) =  (1 + x + x^{2} + x^{3} ....) = 1/x + 1/x^{2} + 1/x^{3} …
And we get out result which we know is false since,
1/x + 1/x^{2} + 1/x^{3} … = 1/(x – 1) can't be true because x = 0 is not allowed on the LHS while it is allowed on the RHS.
If the trend is true then we simply show that (x + x^{2} + x^{3} ....) is 0 when x is 1 and we are left via substitution with (0 + 1  1 = 0).
I am no mathematician so if you find an error above then keep that in mind.If God did not exist, it would be necessary to invent him.  Voltaire
Comment

Originally posted by cisco qid View Post
Not to beat a dead horse to death but if you want to see something really weird  you can actually derive the expression,
...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0, as follows:
Start with the expression:
S = 1/x + 1/x^{2} + 1/x^{3} …
Then
S = 1/x(1 + 1/x + 1/x^{2} + …) = 1/x(1 + S) = 1/x + S/x
or
S  S/x = 1/x => S = 1/(x – 1) = 1/(1x) =  (1 + x + x^{2} + x^{3} ....) = 1/x + 1/x^{2} + 1/x^{3} …
And we get out result which we know is false since,
1/x + 1/x^{2} + 1/x^{3} … = 1/(x – 1) can't be true because x = 0 is not allowed on the LHS while it is allowed on the RHS."The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
Comment

Originally posted by Pragmatic View Post
It is undefined but if you graph the left (make the right y) then the trend is that if n is odd in (1/x^{n} + 1/x ^{n+1}+...) then x approaches 1 as y approaches 1.
If the trend is true then we simply show that (x + x^{2} + x^{3} ....) is 0 when x is 1 and we are left via substitution with (0 + 1  1 = 0).
I am no mathematician so if you find an error above then keep that in mind.
Comment

Originally posted by cisco qid View Post
Not to beat a dead horse to death but if you want to see something really weird  you can actually derive the expression,
...+ 1/x^{3} + 1/x^{2} + 1/x +1 + x + x^{2} + x^{3} +... = 0, as follows:
Start with the expression:
S = 1/x + 1/x^{2} + 1/x^{3} …
Then
S = 1/x(1 + 1/x + 1/x^{2} + …) = 1/x(1 + S) = 1/x + S/x
or
S  S/x = 1/x => S = 1/(x – 1) = 1/(1x) =  (1 + x + x^{2} + x^{3} ....) = 1/x + 1/x^{2} + 1/x^{3} …
And we get out result which we know is false since,
1/x + 1/x^{2} + 1/x^{3} … = 1/(x – 1) can't be true because x = 0 is not allowed on the LHS while it is allowed on the RHS.
Regards, HRG.
"The universe doesn't care what happens to its inhabitants, but its inhabitants do" (Tyrrho).
 1 like
Comment

Originally posted by HRG View Post
That's in effect what I wrote several posts ago. But I won't charge you franchise fees
Last edited by cisco qid; 021218, 06:31 PM.
 1 like
Comment

Originally posted by cisco qid View Post
What you stated was Sx = S and since x is arbitrary S must be zero, which we all now know is false, while I derived the original series. Charging for someone else's intellectual property is copyright infringement.Regards, HRG.
"The universe doesn't care what happens to its inhabitants, but its inhabitants do" (Tyrrho).
Comment

Originally posted by Pragmatic View Post
When I examine graphs that contain a series like (1/x^{n} + 1/x^{n+1}...) if the n is odd then the graph indicates that y = 1 when x = 1. If n is even then y = 0 when x = 1. While I am unsure how to prove this, the trend I see indicates that if (x + x^{2}...) = 0 then you would be left with (1) + 1 + (0) = 0. I am no mathematician so I am ready to be corrected on this.
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x=1..infinity )
infinity
Trying again starting at zero:
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x=0..infinity )
infinity
Trying again from  infinity to + infinity
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x=infinity..infinity )
infinity
"The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
Comment

Originally posted by inertia View Post
Here is what I get when modeled by symbolic Matlab up to the tenth power:
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x=1..infinity )
infinity
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x = 500..500)
Error: Singularity. [sum::sum]
This next one makes sense: From x = 1 to 1
sum(1 + x + x^2 + x^3 + x^4 + x^5+ x^6 + x^7 + x^8 + x^9 + x^10+ 1/x + 1/x^2 + 1/x^3 + 1/x^4 + 1/x^5 + 1/x^6 + 1/x^7 + 1/x^8 + 1/x^9 + 1/x^10,x = 1..1)
Error: Division by zero. [_power]
Evaluating: sum::sum
Getting a result that = 0 was...err...difficult indeed. As expected....
"The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
Comment

Originally posted by Pragmatic View Post
It is undefined but if you graph the left (make the right y) then the trend is that if n is odd in (1/x^{n} + 1/x ^{n+1}+...) then x approaches 1 as y approaches 1.
If the trend is true then we simply show that (x + x^{2} + x^{3} ....) is 0 when x is 1 and we are left via substitution with (0 + 1  1 = 0).
I am no mathematician so if you find an error above then keep that in mind.
It is easy to see why the equation can never provide a sum equaling zero. Thanks for the graphing idea."The exact sciences also start from the assumption that in the end it will always be possible to understand nature, even in every new field of experience, but that we make no a priori assumptions about the meaning of the word "understand"."
Heisenberg
.....................
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge." ( Psalm 19:12 )
 1 like
Comment
Comment