If (1−x)−n=a0+a1x+a2x2+⋯+arxr+⋯, then a0+a1+a2+⋯+ar is equal to

We have,(1−x)−n=a0+a1x+a2x2+⋯+arxr+⋯and (1−x)−1=1+x+x2+x3+⋯+xr+⋯Hence,a0+a1+a2+⋯+ar= Coefficient of xr in the product of the two series = Coefficient of xr in (1−x)−n(1−x)−1= Coefficient of xr in (1−x)−(n+1)=(n+1)(n+2)⋯(n+r)r!=n+rCn