Hi,
Sum[Log[k]/k, {k, 2, N}]
(*StieltjesGamma[1] - StieltjesGamma[1, 1 + N]*)
Note that the second time the functions called with two arguments. If you evaluate:
StieltjesGamma[1] - StieltjesGamma[1, 101] // N
(*10.554*)
which is the same as
Sum[Log[k]/k, {k, 2, 100}]
You are typing in
StieltjesGamma[1] - StieltjesGamma[1]*(1 + 100) // N
instead with evaluates to 7.28158.
So this is not a bug. You just evaluated different function. Note that StieltjesGamma is overloaded: you can use it with one or two input slots.
Cheers,
Marco
