Home
Class 12
MATHS
Prove that (C0+C1)(C1+C2)(C2+C3)(C(n-1)+...

Prove that `(C_0+C_1)(C_1+C_2)(C_2+C_3)(C_(n-1)+C_n)=(n+1)^n/(n!).c_0.C_1.C_2...........C_n`.

Promotional Banner

Similar Questions

Explore conceptually related problems

((C_0 + C_1)(C_1 + C_2)(C_2 + C_3)………(C_(n-1) + C_n) )/(C_0C_1C_2…C_n)

Prove that (C_0 + C_1) (C_1 + C_2) …..(C_(n-1) + C_n) = ((n+1)^n)/(n!) (C_1.C_2.C_3……C_n)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)...(C_(n-1)+C_n)=(C_0C_1C_2...C_(n-1)(n+1)^n)/(n!)

Prove that C_0C_2+C_1C_3+…+C_(n-2)C_n=^(2n)C_(n-2)

Prove that C_0+(C_1)/(2)+(C_2)/(3)+....+(C_n)/(n+1)=(2^(n+1)-1)/(n+1)

Prove that ^n C_0^n C_0-^(n+1)C_1^n C_1+^(n+2)C_2^n C_2-=(-1)^ndot

If C_(0),C_(1),C_(2)…….,C_(n) are the combinatorial coefficient in the expansion of (1+x)^n, n, ne N , then prove that following C_(1)+2C_(2)+3C_(3)+..+n.C_(n)=n.2^(n-1) C_(0)+2C_(1)+3C_(2)+......+(n+1)C_(n)=(n+2)C_(n)=(n+2)2^(n-1) C_(0),+3C_(1)+5C_(2)+.....+(2n+1)C_n =(n+1)2^n (C_0+C_1)(C_1+C_2)(C_2+C_3)......(C_(n-1)+C_n)=(C_0.C_1.C_2....C_(n-1)(n+1)^n)/(n!) 1.C_0^2+3.C_1^2+....+ (2n+1)C_n^2=((n+1)(2n)!)/(n! n!)