Prove by Principle of Mathematical Induction that `(10^(2n -1) + 1)` is divisible by 11 for all `n in N`.

Prove by the principle of mathematical induction that n(n+1)(2n+1) is divisible by 6 for all n in N

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

Prove the following by the principle of mathematical induction: x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N.

Using the principle of mathematical induction, prove that (7^(n)-3^(n)) is divisible by 4 for all n in N .

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

Using principle of mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all nN.

Prove the following by the principle of mathematical induction: 5^(n)-1 is divisible by 24 for all n in N.

Prove by the principle of mathematical induction that n<2^(n) for alln in N

Prove the following by the principle of mathematical induction: 11^(n+2)+12^(2n+1) is divisible 133 for all n in N.

Prove the following by the principle of mathematical induction: 3^(n)+7 is divisible by 8 for all n in N.