If `C_r` stands for `.^nC_r` and `sum_(r=1)^n (r.C_r)/(C_(r-1)) =210` then `n=`
(A) 19
(B) 20
(C) 21
(D) none of these

If sum _(r=1)^n (r^2+1)r! =200xx201! Then n= (A) 200 (B) 201 (C) 199 (D) none of these

sum_(r = 0)^(n-1) (C_r)/(C_r + C_(r+1)) =

Find the sum of sum_(r=1)^n(r^n C_r)/(^n C_(r-1) .

If sum_(r=1)^n t_r= (n(n+1)(n+2))/3 then sum _(r=1)^oo 1/t_r= (A) -1 (B) 1 (C) 0 (D) none of these

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .

If sum_(r=0)^(n)((r+2)/(r+1)).^n C_r=(2^8-1)/6 , then n is (A) 8 (B) 4 (C) 6 (D) 5

Prove that sum_(r = 1)^n r^3 ((n_C_r)/(C_(r - 1)))^2 = (n (n + 1)^2 (n+2))/(12)

Let a= 1/(n!) + sum_(r=1)^(n-1) r/((r+1)!), b= 1/(m!)+sum_(r=1)^(m-1) r/((r+1)!)then a+b= (A) 0 (B) 1 (C) 2 (D) none of these

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If sum_(r=0)^(n-1)(("^nC_r)/(^nC_r+^nC_(r+1)))^3=4/5 then n=