Using mathematical induction, prove the following `n(n+1)(2n+1), n in N` is divisible by 6.

Using mathematical induction,prove the following: 1+2+3+...+n<(2n+1)^(2)AA n in N

Using mathematical induction, prove the following: 1+2+3+...+n< (2n+1)^2 AA n in N

By the Principle of Mathematical Induction, prove the following for all n in N : 10^(2n-1)+1 is divisible by 11.

By the Principle of Mathematical Induction, prove the following for all n in N : a^(2n-1)-1 is divisible by a-1.

By the Principle of Mathematical Induction, prove the following for all n in N : 3^(2n)-1 is divisible by 8 .

By the Principle of Mathematical Induction, prove the following for all n in N : 5^(2n)-1 is divisible by 24.

By the Principle of Mathematical Induction, prove the following for all n in N : 4^(n)-3n-1 is divisible by 9.

By the Principle of Mathematical Induction, prove the following for all n in N : 4^(n)+ 15n-1 is divisible by 9.

By the Principle of Mathematical Induction, prove the following for all n in N : 2^(3n)-1 is divisible by 7 .

Using the principle of mathematical induction, prove each of the following for all n in N (x^(2n)-1) is divisible by (x-1) and (x+1) .