prove-that-1-a-x-n-1-an-x-x-a-

Question Number 17957 by Arnab Maiti last updated on 13/Jul/17

prove that {(1 + \frac{a}{x})}^{n} = (1 + \frac{an}{x}), x ≫ a

Answered by 42 last updated on 13/Jul/17

Expand using binomial theorem :

1 + n (\frac{a}{x}) + \frac{n (n - 1)}{2} {(\frac{a}{x})}^{2} + \dots

Since a ≪ x so {(\frac{a}{x})}^{2}, {(\frac{a}{x})}^{3}, \dots are so

small and can be neglected .

∴ {(1 + \frac{a}{x})}^{n} = 1 + \frac{a n}{x}, provided a ≪ x

Commented by Arnab Maiti last updated on 19/Jul/17

Please solve the question

without using binomial theorem .