Let $r$ and $s$ be two strictly positive natural integers such that $r > s$, and
$$J _ { r , s } = \sum _ { k = 0 } ^ { + \infty } \frac { 1 } { ( r + k + 1 ) ( s + k + 1 ) }$$
Deduce that
$$J _ { r , s } = \frac { 1 } { r - s } \sum _ { k = 0 } ^ { + \infty } \left( \frac { 1 } { s + k + 1 } - \frac { 1 } { r + k + 1 } \right)$$