Infinite series
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06-10-2020, 02:16 AM
Post: #1
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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.
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06-10-2020, 03:53 AM
Post: #2
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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?
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06-10-2020, 08:14 AM
Post: #3
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RE: Infinite series
It works on my G1.
— Ian Abbott |
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06-10-2020, 12:20 PM
Post: #4
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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 TI-50, Casio fx-180P, HP48GX, HP50g, HP Prime G2 |
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06-10-2020, 04:00 PM
Post: #5
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RE: Infinite series
(06-10-2020 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 17B/II/II+ 28S 42S/DM42 32SII 48GX 50g 35s WP34S PrimeG2 WP43S/pilot/C47 Casio, Rockwell 18R |
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06-10-2020, 09:36 PM
Post: #6
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RE: Infinite series
(06-10-2020 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:
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06-11-2020, 02:42 AM
Post: #7
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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?
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06-11-2020, 09:17 AM
Post: #8
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RE: Infinite series
try to delete all values and assumptions of x:
Code:
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06-11-2020, 02:36 PM
Post: #9
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RE: Infinite series
Thanks...that worked. I did not suspect this was the problem since the series worked for odd powers!
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06-11-2020, 04:25 PM
Post: #10
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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 small-letter 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 17B/II/II+ 28S 42S/DM42 32SII 48GX 50g 35s WP34S PrimeG2 WP43S/pilot/C47 Casio, Rockwell 18R |
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06-11-2020, 05:01 PM
Post: #11
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RE: Infinite series
(06-11-2020 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. |
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