MY MATEX NOTES

     This is a quick post sharing the proof of a nice infinite sum involving the Riemann Zeta function that I came across yesterday, namely: (1) Rewrite (1) as let , then (2) (3) Now for particular values we can calculate for , and from (1) , (2) and (3) we have The value of     can be found here , therefore (4) (5) For (6) (7) For (8) (9)

     Following the previous post , we will evaluate today the following two infinite sums from Gradshteyn and Ryzhik Table of Integrals, Series, and Products entries  0.238 1 and 2 We will rely on the the following formulas to compute these two sums: (1) (2) (3) Now we can use (1) and (2) to rewrite the above equation as Or Setting     in (3) we can rewrite Or