If `(nC_0)/(2^n)+2.(nC_1)/2^n+3.(nC_2)/2^n+....(n+1)(nC_n)/2^n=16` then the value of 'n' is

If ""^nC_8=""^nC_2 find the value of 'n'.

(nC_(0))^(2)+(nC_(1))^(2)+(nC_(2))^(2)+......+(nC_(n))^(2)

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to

(nC_(0))^(2)-(nC_(1))^(2)+(nC_(2))^(2)+....+(-1)^(n)(nC_(n))^(2)

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to a. int_0^1x^(n-1)(1-x)^n dx b. int_1^2x^n(x-1)^(n-1)dx c. int_1^2x^(n-1)(1+x)^n dx d. int_0^1(1-x)^(n-1)dx

The value of (nC_(0))/(n)+(nC_(1))/(n+1)+(nC_(2))/(n+2)+......+(nC_(n))/(2n) is equal to

Prove that (2nC_0)^2-(2nC_1)^2+(2nC_2)^2+.....+(2nC_2n)^2=(-1)^n2nC_n

If .^nC_0+3.^nC_1+5^nC_2+7^nC_3+ . . .till (n+1) term=2^100*101 then the value of 2[(n-1)/2] where [.] is G.I.F)

If S_n=^nC_0.^nC_1+^nC_1.^nC_2+.....+^nC_(n-1).^nC_n and if S_(n+1)/S_n=15/4 , then the sum of all possible values of n is (A) 2 (B) 4 (C) 6 (D) 8

If , ^nC_1,^nC_2 and ^nC_3 are in AP. Find the value of n.