The following 2 sums are equal,

a:=sum(ln(1+1/n)/n,n=1..infinity);

                           infinity
                            -----
                             \      ln(1 + 1/n)
                      a :=    )     -----------
                             /           n
                            -----
                            n = 1

b:=sum(ln(n)/n/(n-1),n=2..infinity);

                            infinity
                             -----
                              \        ln(n)
                       b :=    )     ---------
                              /      n (n - 1)
                             -----
                             n = 2

and Maple has no problems evaluating numerically the first one,

evalf(a);

                             1.257746887

but can't evaluate numerically the second one, neither as sum, nor as Sum,

evalf(b);

                          infinity
                           -----
                            \        ln(n)
                             )     ---------
                            /      n (n - 1)
                           -----
                           n = 2

evalf(Sum(ln(n)/n/(n-1),n=2..infinity));

                          infinity
                           -----
                            \        ln(n)
                             )     ---------
                            /      n (n - 1)
                           -----
                           n = 2

Alec