prove using mathematical induction:`-n(n+1)(n+5)` is divisible by `6` for all natural numbers

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

Use the principle of mathematical induction to show that a^(n) - b^9n) is divisble by a-b for all natural numbers n.

using Mathematical induction,prove that 3^(2n)+7 is divisible by 8.

prove that 3^(2n)-1 is divisible by 8, for all natural numbers n.

Prove the following by the principle of mathematical induction: 3^(n)+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 that n(n^(2)+5) is divisible by 6, for each natural number n.

Prove the following by the principle of mathematical induction: 2.7^(n)+3.5^(n)-5 is divisible 25 for all n in N

prove that 4^(n)-1 is divisible by 3, for each natural number n.