Infinite series

06102020, 02:16 AM
Post: #1




Infinite series
Summation of (1/x^3) from x=1 to infinity produces Zeta(3) which is correct, ~1.20206. Why does summation of (1/x^2) from x=1 to infinity produce +/ infinity on my G2? For that matter the summation for 1/x^odd integer produces correct results, incorrect for (1/x^even integer). A summation of (1/x^p) should converge for any p>1.


06102020, 03:53 AM
Post: #2




RE: Infinite series
In home, the summations (1/x^even integer from 1 to infinity) are approximated correctly...why is there a difficulty in CAS?


06102020, 08:14 AM
Post: #3




RE: Infinite series
It works on my G1.
— Ian Abbott 

06102020, 12:20 PM
Post: #4




RE: Infinite series
My G2 also gives, in the CAS, a finite result for 1/x^2, i.e., (pi^2)/6. Anyway, my firmware is not the most recent: 2.0.0.13865 (2018 08 02), so I have to update it.
Ramón Valladolid, Spain TI50, Casio fx180P, HP48GX, HP50g, HP Prime G2 

06102020, 04:00 PM
Post: #5




RE: Infinite series
(06102020 12:20 PM)ramon_ea1gth Wrote: My G2 also gives, in the CAS, a finite result for 1/x^2, i.e., (pi^2)/6. Anyway, my firmware is not the most recent: 2.0.0.13865 (2018 08 02), so I have to update it. Same result for me in the emulator [2.1.14425 (2020 1 16)], and also my G2 [2.1.14433 (2020 01 21)] Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2 & Casios, Rockwell 18R :) 

06102020, 09:36 PM
Post: #6




RE: Infinite series
(06102020 02:16 AM)lrdheat Wrote: Summation of (1/x^3) from x=1 to infinity produces Zeta(3) which is correct, ~1.20206. Why does summation of (1/x^2) from x=1 to infinity produce +/ infinity on my G2? For that matter the summation for 1/x^odd integer produces correct results, incorrect for (1/x^even integer). A summation of (1/x^p) should converge for any p>1. Seeing the above answers you should give us the command line you used. Mine are: Home: Code:
CAS: Code:


06112020, 02:42 AM
Post: #7




RE: Infinite series
When I use the template in CAS, it comes up with +/ infinity if a small “x” is used (as is default in CAS). If I use capital “X” in CAS, I just discovered that the correct pi^2/6 comes up for summation 1/X^2 from 1 to infinity. Why is this, and do I have some setting incorrectly set to produce this odd behavior?


06112020, 09:17 AM
Post: #8




RE: Infinite series
try to delete all values and assumptions of x:
Code:


06112020, 02:36 PM
Post: #9




RE: Infinite series
Thanks...that worked. I did not suspect this was the problem since the series worked for odd powers!


06112020, 04:25 PM
Post: #10




RE: Infinite series
In general, if you want to see/check user variables:
created in Home, := or Sto▸  viewed with memory manager Shift B — User Variables  select, then delete or backspace created in CAS, = or Sto▸  viewed with memory manager Shift B — CAS Vars  select, then delete or backspace  may also be deleted with CAS function purge(), which only works on CAS vars  purge() also removes assumptions about vars, as well as value A couple of CAS programs have been posted on this forum in the past: varslist()  shows all defined lowercase single letter vars, both Home & CAS purgeaz()  purges all single smallletter CAS variables, excluding e & i which are reserved  does not affect Home variables, which can only be deleted using memory manager (shift B) Cambridge, UK 41CL/DM41X 12/15C/16C DM15/16 71B 17B/BII/bII+ 28S 42S/DM42 32SII 48GX 50g 35s 30b/WP34S Prime G2 & Casios, Rockwell 18R :) 

06112020, 05:01 PM
Post: #11




RE: Infinite series
(06112020 02:36 PM)lrdheat Wrote: Thanks...that worked. I did not suspect this was the problem since the series worked for odd powers! Maybe x was assumed to be negative. 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)