Ordinary problem

\[ S = \displaystyle \sum_{n=1}^{\infty} \dfrac{\sigma_{4}(n)}{n^{8}}\]

Find \(\dfrac{\pi^{12}}{S}\).

Notation: \(\sigma_x(n)\) denotes the sum of the \(x^\text{th}\) powers of the positive divisors of \(n\).

Hint: Use Bernoulli numbers to calculate the value of Riemann Zeta function. .

×

Problem Loading...

Note Loading...

Set Loading...