`nC_0 -2.3 nC_1,+3.3^2 nC_2-4.3^3 nC_3+.........+(-1)(n+1) nC_n 3^n` is eqaul to.

Let S=2/1 ^nC_0+2^2/2 ^nC_1+2^3/3 ^nC_2+....+2^(n+1)/(n+1) ^nC_n . Then S equals

Let a=(4^(1/401)-1) and let b_n = nC_1 + nC_2 . a+ nC_3. a^2+......+ nC_n .a^(n-1). Find the value of (b_2006 – b_2005)

The sum of the series 1+(1/2) ^nC_1 +(1/3) ^nC_2 +....+(1/(n+1)) ^nC_n is equal to

If (1 + x)^n= ""^nC_0+""^nC_1x+""^nC_2x^2+.............+ ""^nC_n x^n , prove that : ""^nC_1-2""^nC_2+3""^nC_3-.......+(-1)^(n-1) n ""^nC_n=0 .

If n is a positive integer then (1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _(r=0)^n ^nC_rx^r and (1-x)^n= ^nC_0x^0-^nC_1 x^1 +^nC_2-^nC_3x^3+………+(-1)^n ^nC_nx^n=sum_(r=0)^n (-1)^r ^nC_r x^r On the basis of above information answer the following question:If n is a positive integer then lim_nrarroo n[^nc_n- 2/3 . ^nC_(n-1)+(2/3)^2.^nC_(n-2-...........+(-1)^n(2/3)^n.^nC_n]= (A) 1 (B) 1/2 (C) 0 (D) 1/3

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

Prove that ""^nC_0-2*""^nC_1+3*""^nC_2-...+(-1)""^n(n+1)""^nC_n=0

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_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

nC_(1)+nC_(2)+nC_(3)+............... equals to: