Question

Why is the interval of convergence, for the Taylor series about x=0 for f(u)=(1+u)^(-1/2), equal to |u|<1 ?

Answer 1

\[f(u)=(1+u)^{-\frac{1}{2}}\]

Answer 2

@satellite73 @experimentX

Answer 3

expand that binomially ..

Answer 4

what would the result of that be?

Answer 5

\[ \frac{1}{{\sqrt {1 + x} }} = \sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^{n + 1}}}}{{{2^{2n}}}}} {2n\choose n}{x^n} \]

Answer 6

sorry...not understanding how this is helping