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

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

Using principle of mathematical induction, prove the following 1+3+5+...+(2n-1)=n^(2)

Using the principle of mathematical induction, prove each of the following for all n in N 1+2+3+4+…+N=1/2 N(N+1) .

Using the principle of mathematical induction, prove each of the following for all n in N 3^(n) ge 2^(n)

Using the principle of mathematical induction, prove each of the following for all n in N 2+4+6+8+…+2n=n(n+1) .

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) .

Using mathematical induction prove that n^(2)-n+41 is prime.

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

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

Using the principle of Mathematical Induction, prove that forall nin N , 4^(n) - 3n - 1 is divisible by 9.