Prove that `overset(n)underset(r=0)(Sigma^(n))C_(r).4^(r)=5^(n)`

Answer

N/a

Explanation

Binomial theorem can be written as
`overset(n)underset(r=0)(Sigma).^(n)C_(r).(1)^(n-r)x^(r)=(1+x)^(n)`
`rArr " "overset(n)underset(r=0)(Sigma).^(n)C_(r).x^(r)=(1+x)^(n)`
Putting x=4
`overset(n)underset(r=0)(Sigma).^(n)C_(r).4^(r)=(1+4)^(n)`
`=5^(n)`. Hence proved.