Mathematica 8

Clear[s, n, k]

s = 2;

Table[Sum[n/(k + n - 1)^s - n/(k + n)^s, {k, 1, Infinity}], {n, 1,

12}]

{1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12}

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Mathematica 8

Clear[s, n, k]

s = 2;

Table[Sum[n/(k + n - 1)^s - n/(k + n)^s, {k, 1, Infinity}], {n, 1,

12}]

{1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12}

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