Let `a=(2^(1//401)-1)` and for each `ngeq2,l e tb_n=^n C_1+^n C_2dota+^n C_3a^2+......+^n C_n*a^(n-1)` . Find the value of `(b_(2006)-b_(2005))dot`

Let a=3^(1/(223))+1 and for all tgeq3 , let f(n)=^n C_0dota^(n-1)-^n C_1dota^(n-2)+^n C_2dota^(n-3)-+(-1)^(n-1)dot^n C_(n-1)dota^0 . If the value of f(2007)+f(2008)=3^k w h e r ek in N , then the value of k is.

Find the sum 3^n C_0-8^n C_1+13^n C_2 - 18^n C_3+..

Prove that ^n C_0 ^(2n)C_n- ^n C_1 ^(2n-2)C_n+ ^n C_2^(2n-4)C_n-=2^ndot

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

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

In a triangle A B C ,/_A=60^0a n db : e=(sqrt(3)+1):2, then find the value of (/_B-/_C)dot

If (1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r ,then a= (^n C_2)^2 b. ^n C_rdot^n C_(r+1) c. ^2n C_r d. ^2n C_(r+1)

If (1 - x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + ......... + C_(n)x^(n) , then the value of 1.C_(1) + 2.C_(3) + 3.C_(3) + ......... + n.C_(n) =

Prove that ^m C_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-=(-1)^(m-1)n^mdot

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)