If `A=[(1,1,1),(1,1,1),(1,1,1)]` then show that `A^n=[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))]`.

If A=[(1 1 1),( 1 1 1),( 1 1 1)] , then prove that A^n=|(3^(n-1)3^(n-1)3^(n-1)),(3^(n-1)3^(n-1)3^(n-1)),(3^(n-1)3^(n-1)3^(n-1))| for every positive integer ndot

If A=[[1, 1, 1],[ 1, 1, 1],[ 1, 1, 1]] , prove that A^n=[[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)]], n in N.

Show that (1+3^(- 1))(1+3^(- 2))(1+3^(- 4))(1+3^(- 8)).........(1+3^(-2^n))=3/2(1-3^(-2^((n-1)))) .

Find the sum sum_(n=1)^(oo)(6^(n))/((3^(n)-2^(n))(3^(n+1)-2^(n+1)))

Prove that sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)

Prove that (1)/(1!(n-1)!) + (1)/(3!(n-3)!)+ (1)/(5!(n-5)!) + …….= (2^(n-1))/(n!)

sum_(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n) find n

Find .^(n)C_(1)-(1)/(2).^(n)C_(2)+(1)/(3).^(n)C_(3)- . . . +(-1)^(n-1)(1)/(n).^(n)C_(n)

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^2+5((2n+1)/(2n-1))^3+...