Help me obtain the value of e from (1 + (1/n))^n how do i go about it.


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
Question Number 67659 by Rio Michael last updated on 29/Aug/19

$H e l p m e o b t a i n t h e v a l u e o f e f r o m$ ${(1 + \frac{1}{n})}^{n} h o w d o i g o a b o u t i t .$
Commented by Abdo msup. last updated on 30/Aug/19

$A_{n} = {(1 + \frac{1}{n})}^{n} a n d {l i m}_{n \to + \infty} A_{n} = e$ $A_{n} = \sum_{k = 0}^{n} C_{n}^{k} \frac{1}{n^{k}} = \frac{C_{n}^{0}}{n^{0}} + \frac{C_{n}^{1}}{n^{1}} + \frac{C_{n}^{2}}{n^{2}} + \frac{C_{n}^{3}}{n^{3}} + . . + \frac{C_{n}^{n}}{n^{n}} \Rightarrow$ $e = {l i m}_{n \to + \infty} A_{n} = 1 + 1 + \frac{C_{n}^{2}}{n^{2}} + \frac{C_{n}^{3}}{n^{3}} + . . . .$ $= 2 + \frac{n (n - 1)}{2 n^{2}} + \frac{n (n - 1) (n - 2)}{6 n^{3}} + . . .$ $w d f i n d e \sim 2, 7 . . .$
Commented by Rio Michael last updated on 30/Aug/19

$t h a n k s s i r$
Commented by Abdo msup. last updated on 30/Aug/19

$y o u a r e w e l c o m e .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum