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

If sum_(r=0)^(n){("^(n)C_(r-1))/('^(n)C_(r )+^(n)C_(r-1))}^(3)=(25)/(24) , then n is equal to (a) 3 (b) 4 (c) 5 (d) 6

The vaule of sum_(r=0)^(n-1) (""^(C_(r))/(""^(n)C_(r) + ""^(n)C_(r +1)) is equal to

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

Statement -2: sum_(r=0)^(n) (-1)^( r) (""^(n)C_(r))/(r+1) = (1)/(n+1) Statement-2: sum_(r=0)^(n) (-1)^(r) (""^(n)C_(r))/(r+1) x^(r) = (1)/((n+1)x) { 1 - (1 - x)^(n+1)}

If n in N, then sum_(r=0)^(n) (-1)^(n) (""^(n)C_(r))/(""^(r+2)C_(r)) is equal to .

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

sum_(r=0)^n (-1)^r .^nC_r (1+rln10)/(1+ln10^n)^r

The value of sum_(r=0)^(3n-1)(-1)^r ^(6n)C_(2r+1)3^r is

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

If S_n=sum_(r=0)^n 1/(nC_r) and t_n=sum_(r=0)^n r/(nC_r), then t_n/S_n=