Fun. For the skeptic - +/ ( (2^~]) % 2&^) i.1e5 6
Not infinity but still can be used to validate On Oct 24, 2014 11:32 AM, "Jon Hough" <[email protected]> wrote: > I was trying to remember how to solve a math problem the other day, and I > got the chance to use the verb d. . > The problem is > find the sum(k= 0, k = infinity) of (k^2)/(2^k) > I don't know the best way to solve it, the method I employed was to do: > define > S(x) as the sum(k= 0, k = infinity) of (k^2)*EXP(x * k), defined for > x < 0 > then integrate w.r.t. x twice (ignoring constants of integration) > D^(-2)S(x) = the sum(k= 0, k = infinity) of EXP(x * k) > This is a geometric sum, so can be rewritten > D^(-2)S(x) = 1 / (1 - EXP(x)) > Then, to rewrite S(x), we just need to differentiate twice w.r.t x. This > is tiresome doing by hand, so I employed J: > > f =: %@:(1&+)@:(_1&*)@:^ > > > > > f d. 2 (^. 0.5) > > > which gives the answer: 6. > > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
