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Tag Archives: Real Analysis
Let denote the zeta function. Prove that
We are working near . It follows from the Integral Comparison Test that
The result follows from the Sandwich Theorem.
Evaluate the double sum
We sum diagonally , hence:
(1): For it holds .
Conjecture: Does the following equality
Evaluate the series
One can argue that the same technique used to evaluate the sum here can be used here as well. Unfortunately, this is not the case as the sum does not telescope. However the technique used here is the way to go.
First of all we note that
However, it is known that
Let . We note that . Hence,
which is now a matter of calculations. The sum is equal to