Using mathematical induction prove that `10^(2n-1)+1` is divisible by 11 for all `n in N`

Using mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all n in N

(a)Prove that 3^(2n)-1 is divisible by 8.

Using the principle of Mathematical induction,prove that 10^(2n-1)+1 is divisible by 11.

Using mathematical induction prove that 41^n-14^n is a multiple of 27 for all n in N

Using principle of mathematical induction prove that n(n+1)(n+5) is a multiple of 3 for all n in N .

By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) is divisible by 7 is true for all n in N

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

Using mathematical induction prove that (1+1/1)(1+1/2)(1+1/3)......(1+1/n)=n+1 for all n in N

Using mathematical induction prove that d/(d x)(x^n)=n x^(n-1) for all positive integers n .

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .