Sums and products

[New] Problem : find a closed-form for .

>> Factor(sum(k^3,k=1..n));

                                   2        2
                              1/4 n  (n + 1)

[New] Problem : find a closed-form for .

>> sum(1/k^2+1/k^3,k=1..infinity);

                                           2
                                         PI 
                               zeta(3) + ---
                                          6