log1-1-log3-3-log5-5-log7-7-

Question Number 121653 by Dwaipayan Shikari last updated on 10/Nov/20

\frac{l o g 1}{\sqrt{1}} - \frac{l o g 3}{\sqrt{3}} + \frac{l o g 5}{\sqrt{5}} - \frac{l o g 7}{\sqrt{7}} + \dots .

Commented by TANMAY PANACEA last updated on 10/Nov/20

e x c e l l e n t q u e s t i o n b u t s t i l l t h i n k i n g h o w t o s t a r t

Commented by Dwaipayan Shikari last updated on 10/Nov/20

R a m a n u j a n s h o w e d t h a t t h e r e s u l t i s

(\frac{π}{4} - \frac{γ}{2} - \frac{l o g (2 π)}{2}) (\frac{1}{\sqrt{1}} - \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{5}} - \frac{1}{\sqrt{7}} + \dots . + C)

I s t h e r e a n y w a y t o p r o v e ?

γ = 0.5771 (E ULER MASCHERONI)

γ = \lim_{n \to \infty} \underset{k = 1}{\sum^{n}} \frac{1}{k} - l o g (n)

Commented by TANMAY PANACEA last updated on 10/Nov/20

e x c e l l e n t \dots d i d y o u h e a r d n a m e o f M r . H a r d y

Commented by TANMAY PANACEA last updated on 10/Nov/20

Commented by Dwaipayan Shikari last updated on 10/Nov/20

Y e s s i r!