Sum with alternate signs
02-06-2015, 05:08 PM (This post was last modified: 02-06-2015 05:17 PM by Gilles.)
Post: #4
 Gilles Member Posts: 226 Joined: Oct 2014
RE: Sum with alternate signs
(02-06-2015 02:26 PM)salvomic Wrote:  hi,
there is a way in Prime to do this sum?
$\sum_{k=1}^{\infty}{\frac {(-1)^{k+1}}{k^{2}} }$

the value is $$\frac {π^{2}}{12}$$

HP Prime gives symbolic form, not the value of the sum...

Thanks

Salvo

You can do

$\sum_{k=1}^{\infty}{\frac {-1}{(2*k)^{2}} } + \sum_{k=1}^{\infty}{\frac {1}{(2*k-1)^{2}} }$

By the way I get the correct answer on the HP50G but my Prime seems unable to calculate Psi(1/2,1) in a numeric value.

I get :

1/4*Psi(1/2,1)-Pi²/24

Same on 50G then ->NUM returns 0.8224...
On the Prime ~ don't 'solve' Psi(0.5,1) . Strange ...
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 Messages In This Thread Sum with alternate signs - salvomic - 02-06-2015, 02:26 PM RE: Sum with alternate signs - retoa - 02-06-2015, 04:47 PM RE: Sum with alternate signs - salvomic - 02-06-2015, 04:49 PM RE: Sum with alternate signs - Gilles - 02-06-2015 05:08 PM RE: Sum with alternate signs - salvomic - 02-06-2015, 05:18 PM RE: Sum with alternate signs - retoa - 02-06-2015, 05:10 PM RE: Sum with alternate signs - parisse - 02-06-2015, 06:55 PM RE: Sum with alternate signs - salvomic - 02-06-2015, 07:03 PM RE: Sum with alternate signs - parisse - 02-07-2015, 06:46 AM RE: Sum with alternate signs - salvomic - 02-07-2015, 10:11 AM RE: Sum with alternate signs - salvomic - 05-13-2015, 08:09 PM

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