how-can-we-expand-1-x-1-2-

Question Number 13327 by Nayon last updated on 18/May/17

h o w c a n w e e x p a n d {(1 + x)}^{\frac{1}{2}} ? ?

Answered by prakash jain last updated on 19/May/17

{(1 + x)}^{y} = 1 + y x + \frac{y (y - 1)}{2!} x^{2} + \frac{y (y - 1) (y - 2)}{3!} x^{3} +

\dots t o i n f i n i t y

The above series expansion

is valid for ∣ x ∣< 1 (f o r c o n v e r g e n c e)

{(1 + x)}^{1 / 2} = 1 + \frac{1}{2} x + \frac{\frac{1}{2} (\frac{1}{2} - 1)}{2!} x^{2} + \dots