If n is a positive integer, prove that `underset(nrarrinfty)Lim(Sigman)/(n^2) = 1/2`.

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is

underset(nrarrinfty)lim (1^2+2^2+3^2+………+n^2)/n^3 is equal to:

For an positive integer n, prove that : i^(n) + i^(n+1) + i^(n+2) + i^(n+3) + i^(n+4) + i^(n + 5) + i^(n+6) + i^(n+7) = 0 .

For every positive integer n, prove that 7^n-3^n is divisible by 4.

underset(xrarra)lim (x^n-a^n)/(x-a) is equal to:

The coefficient of x^n , where n is any positive integer, in the expansion of (1+2x+3x^2 +... to oo)^(1//2) is:

If n is any positive integer , show that 2^(3n +3) -7n - 8 is divisible by 49 .

Prove by induction that if n is a positive integer not divisible by 3 , then 3^(2n)+3^(n)+1 is divisible by 13 .