Calculus 1

Calculus Level 4

$\large \sum_{n=1}^\infty \dfrac {(-1)^{n-1} }{n^{1729}} = (1-2^{-a}) \zeta(b)$

The equation above holds true for positive integers $a$ and $b$ . Find $a+b$ .

Notation : $\zeta(\cdot)$ denotes the Riemann zeta function .

The answer is 3457.

1 solution

Kunal Gupta
Sep 29, 2016

This is simply, the Dirichlet Eta Function , defined as: $\eta(s)=\displaystyle \sum_{k=1}^{\infty}\dfrac{(-1)^{k-1}}{k^{s}}=(1-2^{1-s})\zeta(s)$ For our case, $a=1728$ and $b=1729$ , summing up to $3457$

Calculus 1

The answer is 3457.

1 solution

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