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)

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.1! +2.2! +3.3! +.......+ n.n! = (n+1)!-1 .

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

By Mathematical Induction, prove that : n! 1 .

Using principle of mathematical induction, prove that 1 + 3 + 3^(2) + … 3^(n-1) = (3^(n) - 1)/(2)

Using mathematical induction prove that P(n) = 1+3+5+........... +2n-1=n^(2)

Using mathematical induction, to prove that 1*1!+2*2!+3.3!+ . . . .+n*n! =(n+1)!-1 , for all n in N