Dirichlet series summation for zeta

by user1828958   Last Updated March 10, 2019 16:20 PM - source

This question is a bit different from one another online. It appear in reppresenting Dirichlet series

Do you know how the following equation is true?

$$\sum_{1}^{\infty} \frac{1}{n^s} = \sum_{1}^{\infty} n \cdot \big (\frac{1}{n^s} - \frac{1}{(n+1)^s} \big)$$

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Modulus of Riemann zeta function.

Updated December 28, 2018 14:20 PM

Alternating Bertrand series

Updated March 21, 2019 02:20 AM