Homework$-9$: Problem $12$

$(6$ points$)$

Use the following binomial series formula

$(1+x{)}^m=1+mx+\frac{m(m-1)}{2!}{x}^2+$cdots$+\frac{m(m-1)cdots(m-k+1)}{k!}{x}^k+$cdots

to obtain the MacLaurin series for

$($a$)\frac{1}{(1+x{)}^6}={\displaystyle \underset{k=0}{\overset{}{}}}$

$($b$)\sqrt[6]{1+x}=,+$cdots. Enter first $4$ terms only.