Let denote the
-th harmonic sum. Prove that
where denotes the Riemann zeta function.
Solution
Nothing more than a series manipulation. Successively we have:
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Let denote the
-th harmonic sum. Prove that
where denotes the Riemann zeta function.
Solution
Nothing more than a series manipulation. Successively we have:
Recalling the fact that
we note that the series
diverges.