Prove that `2 + 4 + 6 + .... + 2n = n (n + 1)`

Prove the following by the method of induction for all n in N : 2 + 4 + 6 +... +2n = n(n + 1).

Prove 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1), AA n in N

By method of induction prove that 1.3 + 2.5 + 3.7 +...+ n (2n + 1) = n/6 (n + 1) (4n + 5) for all n in N

For all n gt= 1 , prove that, 1^2 + 2^2 + 3^2 + 4^2 + …….+n^2 = (n(n+1)(2n+1))/(6)

Prove that 2.4.6.8..........2n<(n+1)^(n)*(n in N)

Prove that 1*2+2*3+3*4+.....+n*(n+1)=(n(n+1)(n+2))/(3)

If n ge 1 is a positive integer, then prove that 3^(n) ge 2^(n) + n . 6^((n - 1)/(2))

Prove the following by using the principle of mathematical induction for all n in N : 1. 2. 3 + 2. 3. 4 + .. . + n(n + 1) (n + 2)=(n(n+1)(n+2)(n+3))/4