evaluate-0-1-0-1-0-1-0-1-0-1-da-db-dc-dd-df-1-abcdf-

Question Number 132091 by rs4089 last updated on 11/Feb/21

e v a l u a t e

\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \frac{d a . d b . d c . d d . d f}{1 - a b c d f}

Answered by Dwaipayan Shikari last updated on 11/Feb/21

\underset{n = 1}{\sum^{\infty}} \frac{1}{n^{5}} = ζ (5)

Answered by Dwaipayan Shikari last updated on 11/Feb/21

\underset{n = 0}{\sum^{\infty}} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} {(a b c d f)}^{n} d a d b d c d d d f

= \underset{n = 0}{\sum^{\infty}} \frac{1}{{(n + 1)}^{5}} = ζ (5)