prove-that-1-1-2-1-3-1-4-1-5-1-n-1-n-is-always-positive-

Question Number 96951 by aurpeyz last updated on 05/Jun/20

p r o v e t h a t 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} + \dots + \frac{- 1^{n - 1}}{n} i s a l w a y s p o s i t i v e

Commented by mr W last updated on 05/Jun/20

h o w m a n y t i m e s d o y o u w a n t t o p o s t

t h e s a m e q u e s t i o n ? b e s i d e s t h e

q u e s t i o n i s a l r e a d y a n s w e r e d . i f y o u

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t h e o r i g i n a l q u e s t i o n a n d a n s w e r,

i n s t e a d o f p o s t i n g t h e s a m e q u e s t i o n

a s e c o n d o r t h i r d t i m e . t h a n k y o u!

Commented by mr W last updated on 05/Jun/20

a n s w e r i n Q 95473

Commented by mr W last updated on 05/Jun/20

y o u c a n c l i c k o n t h e f u n e l i c o n o n t h e

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q u e s t i o n {I D}^{″} a n d t h e n e n t e r t h e n o .

o f t h e q u e s t i o n y o u w a n t t o g o t o .

b u t i n t h i s c a s e a c o m m a n d b a r i s

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o n i t!

Commented by aurpeyz last updated on 05/Jun/20

i a m s o r r y . i a m n e w t o t h i s p l a t f o r m

Commented by aurpeyz last updated on 05/Jun/20

h o w d o i g e t t o q 95473 ?

Answered by Sourav mridha last updated on 06/Jun/20

l n (1 + x) = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n} . x^{n}

n o w p u t t i n g x = 1 y o u g e t . .

\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n} = l n 2 \approx 0.693 > 0