Asked by lilly
Find the first four term in the expense of (1+x)-½
Answers
Answered by
mathhelper
The general expansion of (1+x)^n
= 1 + nx + n(n−1)/2! x^2 + n(n-1)(n-2)/3! x^3 + ...
so (1+x)^(-1/2)
= 1 + (-1/2)x + (-1/2)(-1/2-1)/2! x^2 - (-1/2)(-1/2 - 1)(-1/2 - 2)/3! x^3 + ....
= 1 - (1/2)x + (3/8)x^2 - (5/16)x^3 + ...
= 1 + nx + n(n−1)/2! x^2 + n(n-1)(n-2)/3! x^3 + ...
so (1+x)^(-1/2)
= 1 + (-1/2)x + (-1/2)(-1/2-1)/2! x^2 - (-1/2)(-1/2 - 1)(-1/2 - 2)/3! x^3 + ....
= 1 - (1/2)x + (3/8)x^2 - (5/16)x^3 + ...