Question

expand (1+1)^n by using binomial theorem and then simplify

Answer 1

I think I already answered this:
\[n!/n! + n!/((n-1)!(1!))+n!/((n-2!)(2!))+...+(n!)/((1!)(n-1)!)+ n!/n!\]

Answer 2

here \[t _{r}=C _{n}^{r}\]
\[s_{r}=\sum_{r=0}^{n}t _{r}\]
nC0+nC1+nC2+....nCn=2^n.
so simplifying you get 2^n. this is quiet obvious from the above relation that (1+1)^n=2^n