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unsum

Run Example
(%i1)sum (n^4*4^n/binomial(2*n,n), n, 0, inf);
                            inf
                            ====        4  n
                            \          n  4
(%o1)                        >    ----------------
                            /     binomial(2 n, n)
                            ====
                            n = 0
(%i2)  unsum (%, n);
(%o2)                                  0
(%i3)  unsum (prod (i^2, i, 1, n), n);
                           n - 1
                           /===\
                            ! !   2
(%o3)                     ( ! !  i ) (n - 1) (n + 1)
                            ! !
                           i = 1
(%i4)  nusum (%, n, 1, n);
(%o4)            
Run Example
simplify_sum(sum(1/(k^2), k, 1, inf));
                                         inf
                                         ====
                                         \     1
(%o1)                       simplify_sum( >    --)
                                         /      2
                                         ====  k
                                         k = 1
(%i2)  nusum ((binomial(n,k))^2/binomial(2*n,n), n, 0, n);
                             n
                            ====          2
                            \     binomial (n, k)
(%o2)                        >    ----------------
                            /     binomial(2 n, n)
                            ====
                            n = 0
(%i3)  unsum (%, n);
(%o3)                                  0
(%i4)  unsum (prod (i^2, i, 1, n), n);
                           n - 1
                           /===\
                            ! !   2
(%o4)                     ( ! !  i ) (n - 1) (n + 1)
                            ! !
                           i = 1
(%i5)  nusum (%, n, 1, n);
(%o5)            
Run Example
nusum (n*n!, n, 0, oo);

solve: dependent equations eliminated: (1)
(%o1)                            (oo + 1)! - 1
(%i2)  nusum (n^4*4^n/binomial(2*n,n), n, 0, n);
                           4        3       2              n
            2 (n + 1) (63 n  + 112 n  + 18 n  - 22 n + 3) 4     2
(%o2)       ------------------------------------------------ - ---
                          693 binomial(2 n, n)                 231
(%i3)  unsum (%, n);
(%o3)                                  0
(%i4)  unsum (prod (i^2, i, 1, n), n);
                           n - 1
                           /===\
                            ! !   2
(%o4)                     ( ! !  i ) (n - 1) (n + 1)
                            ! !
                           i = 1
(%i5)  nusum (%, n, 1, n);
(%o5)            

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