prove that 1−(1/2)+(1/3)−(1/4)+(1/5)+...+((−1^(n−1) )/n) is always positive


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 96951 by aurpeyz last updated on 05/Jun/20

$p r o v e t h a t 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} + . . . + \frac{- 1^{n - 1}}{n} i s a l w a y s p o s i t i v e$
Commented by mr W last updated on 05/Jun/20

$h o w m a n y t i m e s d o y o u w a n t t o p o s t$ $t h e s a m e q u e s t i o n ? b e s i d e s t h e$ $q u e s t i o n i s a l r e a d y a n s w e r e d . i f y o u$ ${d o n}^{'} t u n d e r s t a n d t h e a n s w e r, p l e a s e$ $g i v e f e e d b a c k i n t h e s a m e t h r e a d a s$ $t h e o r i g i n a l q u e s t i o n a n d a n s w e r,$ $i n s t e a d o f p o s t i n g t h e s a m e q u e s t i o n$ $a s e c o n d o r t h i r d t i m e . t h a n k y o u!$
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

$y o u c a n c l i c k o n t h e f u n e l i c o n o n t h e$ $t o p o f t h e s c r e e n a n d s e l e c t ‘ ‘ G o t o$ $q u e s t i o n {I D}^{″} a n d t h e n e n t e r t h e n o .$ $o f t h e q u e s t i o n y o u w a n t t o g o t o .$ $b u t i n t h i s c a s e a c o m m a n d b a r i s$ $a u t o m a t i c a l l y g e n e r a t e d, j u s t t a p$ $o n i t!$
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

	$l n (1 + x) = \underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n} . x^{n}$ $n o w p u t t i n g x = 1 y o u g e t . .$ $\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n - 1}}{n} = l n 2 \approx 0.693 > 0$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum