The following sum was calculated.
In[1]:= Sum[(1 - k/(n + 2))^(1/n), {k, 1, n}] // Simplify
Out[1]= (-(1/(2 + n)))^(1/n) (-HurwitzZeta[-(1/n), -1] + HurwitzZeta[-(1/n), -1 - n])
and,
In[2]:= % /. n -> 100.
Out[2]= 98.8711 + 6.22044 I
But,
In[3]:= n = 100.; Sum[(1 - k/(n + 2))^(1/n), {k, 1, n}]
Out[4]= 99.0666
What's happend?
n >= k, and n and k are integers.
Is it necessary to put a condition in the former sum?
