1-2-2-1-1-2-2-2-2-1-1-2-1-3-2-2-3-1-1-2-1-3-1-4-2-2-4-Find-in-a-closed-form-

Question Number 134984 by Dwaipayan Shikari last updated on 09/Mar/21

\frac{1^{2}}{2} + \frac{{(1 + \frac{1}{2})}^{2}}{2^{2}} + \frac{{(1 + \frac{1}{2} + \frac{1}{3})}^{2}}{2^{3}} + \frac{{(1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4})}^{2}}{2^{4}} + \dots

Find in a closed form

Answered by Ñï= last updated on 09/Mar/21

\underset{n = 1}{\sum^{\infty}} \frac{H_{n}^{2}}{2^{n}} = \frac{1}{1 - \frac{1}{2}} [{l n}^{2} (1 - \frac{1}{2}) + {L i}_{2} (\frac{1}{2})] = 2 {l n}^{2} 2 + 2 {L i}_{2} (\frac{1}{2}) = {l n}^{2} 2 + \frac{π^{2}}{6}

H_{n} : h a r m o n i c n u m b e r

Commented by Dwaipayan Shikari last updated on 09/Mar/21

G r e a t s i r!

Answered by mnjuly1970 last updated on 09/Mar/21

Commented by Dwaipayan Shikari last updated on 09/Mar/21

G r e a t s i r! T h a n k i n g y o u!

Commented by mnjuly1970 last updated on 09/Mar/21

g r a t e f u l \dots