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

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 4^(n)+ 15n - 1 is divisible 9 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 Ndot

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

Use the Principle of Mathematical Induction to prove that n(n + 1) (2n + 1) is divisible by 6 for all n in N.

Prove by the principle of mathematical induction that for all n in N. 3^(2n)+7 is divisible by 8 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.

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 for all n in N. 5^(2n)-1 is divisible by 24 for all n in N .

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