Sum with alternate signs - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Sum with alternate signs (/thread-3024.html) Sum with alternate signs - salvomic - 02-06-2015 02:26 PM 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 RE: Sum with alternate signs - retoa - 02-06-2015 04:47 PM Same problem in xcas and Maxima. Wolframalpha gives the right answer. RE: Sum with alternate signs - salvomic - 02-06-2015 04:49 PM (02-06-2015 04:47 PM)retoa Wrote:  Same problem in xcas and Maxima. Wolframalpha gives the right answer. yes, in fact! As I like much more Prime (and HP 50g), I wonder why they don't... RE: Sum with alternate signs - Gilles - 02-06-2015 05:08 PM (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 ... RE: Sum with alternate signs - retoa - 02-06-2015 05:10 PM I also tried to decompose it in $$\sum_{k=1}^{\infty}(\frac{1}{(2k-1)^2}-\frac{1}{(2k)^2})$$ to avoid the (-1)^(k+1), but I did not get the wanted result. Still the Psi(1/2,1) RE: Sum with alternate signs - salvomic - 02-06-2015 05:18 PM (02-06-2015 05:08 PM)Gilles Wrote:  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. thanks a lot, Gilles, yes I see that Prime don't approx Psi1/2,1); my HP50 does it. Hope in a next firmware to have the symbolic result (π^2/12), more interesting than Psi() RE: Sum with alternate signs - parisse - 02-06-2015 06:55 PM Indeed, for the approx value of Psi(x,1), Xcas calls the GSL, that is not available on the Prime. RE: Sum with alternate signs - salvomic - 02-06-2015 07:03 PM (02-06-2015 06:55 PM)parisse Wrote:  Indeed, for the approx value of Psi(x,1), Xcas calls the GSL, that is not available on the Prime. I understand. There is no other way to approximate Psi on Prime? thank you RE: Sum with alternate signs - parisse - 02-07-2015 06:46 AM No built-in yet. Maybe I'll implement something, in the meantime you can write a user program http://people.math.sfu.ca/~cbm/aands/page_260.htm RE: Sum with alternate signs - salvomic - 02-07-2015 10:11 AM (02-07-2015 06:46 AM)parisse Wrote:  No built-in yet. Maybe I'll implement something, in the meantime you can write a user program http://people.math.sfu.ca/~cbm/aands/page_260.htm ok, thank you for information! I'll think to write a program, maybe... RE: Sum with alternate signs - salvomic - 05-13-2015 08:09 PM the problem is now solved with the firmware 7820! Answer: -π/12