Prove that `2^n >1+nsqrt(2^(n-1)),AAn >2` where `n` is a positive integer.

Prove that 2^(n)>1+n sqrt(2^(n-1)),AA n>2 where n is a positive integer.

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .

if A =[(3,-4),( 1,-1)] then prove that A^n = [ ( 1+2n, -4n),( n,1-2n)] where n is any positive integer .

If A=[(3,-4),(1,-1)] , then prove that A^(n)=[(1+2n,-4n),(n,1-2n)] , where n is any positive integer.

If A=[[3,-4],[1,-1]] , then prove that A^n=[[1+2n,-4n],[n,1-2n]] , where n is any positive integer.

if A=[[3, -4],[ 1, (-1)]] , then prove that A^n=[[1+2 n, -4 n ],[n , 1-2n]] where n is any positive integer.

If A=[{:(3,-4),(1,-1):}] , then prove that A^(n)=[{:(1+2n,-4n),(n,1-2n):}] where n is any positive integer .

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

By using binomial theorem prove that (2^(3n)-7n-1) is divisible by 49 where n is a positive integer.

Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer, where n is a positive integer. (JEE-2004]