Sum with alternate signs

[Gilles]

(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 ...