\[\sum\limits_{n = 1}^\infty {\frac{{{\zeta _n}\left( 7 \right)}}{{{n^2}}}{{\left( { - 1} \right)}^{n - 1}}} = ?\;\;\]

\[{\zeta _n}\left( s \right) = \sum\limits_{k = 1}^n {\frac{1}{{{k^s}}}} .\]

Board index **‹** Computation of Series **‹** How to obtain the closed form of Euler sum
## How to obtain the closed form of Euler sum

\[\sum\limits_{n = 1}^\infty {\frac{{{\zeta _n}\left( 7 \right)}}{{{n^2}}}{{\left( { - 1} \right)}^{n - 1}}} = ?\;\;\]

\[{\zeta _n}\left( s \right) = \sum\limits_{k = 1}^n {\frac{1}{{{k^s}}}} .\]

**Moderators:** galactus, sos440, zaidalyafey

1 post
• Page **1** of **1**

\[{\zeta _n}\left( s \right) = \sum\limits_{k = 1}^n {\frac{1}{{{k^s}}}} .\]

1 post
• Page **1** of **1**