prove-that-1-n-1-2n-1-1-n-3-2-ln-pi-2-n-2-1-n-n-1-1-n-3-2-2-ln-8pi-2-3-n-1-

Question Number 165418 by mnjuly1970 last updated on 01/Feb/22

p r o v e t h a t :

1^{*} : \underset{n = 1}{\sum^{\infty}} \frac{ζ (2 n) - 1}{1 + n} = \frac{3}{2} - \ln (π)

2^{* *} : \underset{n = 2}{\sum^{\infty}} \frac{{(- 1)}^{n} (ζ (n) - 1)}{1 + n} = \frac{3}{2} + \frac{γ}{2} - \frac{\ln (8 π)}{2}

3^{* *} : \underset{n = 1}{\sum^{\infty}} \frac{ζ (2 n) - 1}{1 + 2 n} = \frac{3}{2} - \frac{\ln (4 π)}{2}

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