The coefficient of x5 in the expansion of (1+x)21+(1+x)22+(1+x)23 +........... + (1+x)30 is
51C5
9C5
31C6-21C6
31C6+20C5
(1+x)21+(1+x)22+…+(1+x)30=(1+x)21(1+x)10−1(1+x)−1=1x(1+x)31−(1+x)21⇒ Coefficient of x5 in the given expression = Coefficient of x5 in 1x(1+x)31−(1+x)21 = Coefficient of x6 in (1+x)31−(1+x)21 =31C6−21C6