Question

Evaluate:

$\sum _{r=0}^{20}{}^{20}{C}_r$.

Answer 1

We've,

$(1+x{)}^n={}^n{C}_0{+}^n{C}_{1}x+......{+}^n{C}_n{x}^n$.

Now putting $n=20$ and $x=1$ we get,

$2^{20}=\sum _{r=0}^{20}{}^{20}{C}_r$.