Prove thatnC0+ 2.nC1+ 3.nC2+ ........... +(n+1).nCn= (n+2).2( n-1). Share with your friends Share 0 Ishwarmani answered this Dear Student, Please find below the solution to the asked query: C0n+2·C1n+3·C2n+......+n+1·Cnn Its rth term is tr = r·Cr-1n =r-1+1·Cr-1n =r-1·Cr-1n+1·Cr-1n =n·Cr-2n-1+Cr-1n as r-1·Cr-1n=n.Cr-2n-1 C0+2·C1n+3·C2n+......+n+1·Cnn = ∑r = 1n+1tr⇒ ∑r = 1n+1tr =∑r = 1n+1 n·Cr-2n-1+∑r = 1n+1Cr-1n =n∑r = 1n+1 Cr-2n-1+∑r = 1n+1Cr-1n =nC0n-1+C1n-1+......+Cn-1n-1+C0n+C1n+......+Cnn =n·2n-1+2n =n+22n-1Hope this information will clear your doubts about the topic. If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible. 2 View Full Answer