1-1-2-1-3-1-4-1-5-1-6-1-7-Find-the-sum-

Question Number 99889 by Dwaipayan Shikari last updated on 23/Jun/20

1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \dots \dots . \infty {Find the sum}

Answered by smridha last updated on 23/Jun/20

t h i s i s c a l l e d H a r m o n i c s e r i e s

a n d H a r m o n i c s e r i e s a l w a y s

d i v e r g e s o i t h a s n o f i n i t e v a l u e

H_{n} = \underset{n = 1}{\sum^{\infty}} \frac{1}{n} = \infty

i f t h e s e r i e s i s l i k e t h a t :

1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots \infty = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n} {(1)}^{n}

= l n (2) \approx 0.693

Commented by Dwaipayan Shikari last updated on 23/Jun/20

O h h i t i s a l o g a r i t h m i c s e r i e s . T h a n k i n g y o u