The value of `(n!)^n ` if `n+(n-1)+(n-2)=n(n-1)(n-2)`, where `n^3 >9` ,a positive number is

Find the value of (-1)^(n)+(-1)^(2n)+(-1)^(2n_1)+(-1)^(4n+2) , where n is any positive and integer.

What are the limits of (2^(n)(n+1)^(n))/(n^(n)) , where n is a positive integer ?

The value of ((243)^(n/5). 3^(2n+1))/(9^(n).3^(n-1)) is:

Show that the middle term in the expansion of (1+x)^(2n) is (1.3.5...*(2n-1))/(n!)2nx^(n)2nx^(n) where n is a positive integer.

P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisible by -

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 .

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

Find the value of (3^(n)xx3^(2n+1))/(9^(n)xx3^(n-1)) .