`n+(n-1)x+(n-2)x^2+........+2x^(n-2)+x^(n-1).`

Find the sum to n terms of the series n+(n-1)x+(n-2)x^(2)+.........+2x^(n-2)+x^(r)

The sum of : (x+ 2)^(n-1) + ( x+2) ^(n-2) (x+1) + ( x+2)^(n-3) (x+1)^(2) + "......." + ( x+ 1)^(n-1) equals :

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1) (x+2)^(n-2)-(x+1)^n b. (x+2)^(n-2)-(x+1)^(n-1) c. (x+2)^n-(x+1)^n d. none of these

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is

If I_(n)=int_(0)^(1)(1+x+x^(2)+....+x^(n-1))(1+3x+5x^(2)+....+(2n-3)x^(n-2)+(2n-1)x^(n-1))dx,n in N, then the value of sqrt(I_(9)) is

Find the value of (1+x)^(n)+nc_(1)(1+x)^(n-1)*(1-x)+^(n)C_(2)(1+x)^(n-2)(1-x)^(2)+.........+(1-x)^(n)

Divide x^(2n)+a^(2^(n-1))x^(2^(n-1))+a^(2^(n))byx^(2^(n-1))-a^(2^(n-2))x^(2^(n-2))+a^(2^(n-1))

Coefficient of x^(n-1) in the expansion of.(x+3)^(n)+(x+3)^(n-1)(x+2)+(x+3)^(n-2)(x+2)^(2)+.........+(x+2)^(n) is :

Prove,by induction,that (nC_(0))/(x)-(nC_(1))/(x+1)+(nC_(2))/(x+2)-.........+(-1)^(n)*(nC_(n))/(x+n)=(n!)/(x(x+1)(x+2)......(x+n)),x in