Prove that :`1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6`

Prove the following by the principle of mathematical induction: 1^(2)+2^(2)+3^(2)++n^(2)=(n(n+1)(2n+1))/(6)

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

Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2) .

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

Prove that : 1^(3)+2^(3)+3^(3)++n^(3)={(n(n+1))/(2)}^(2)

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

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

Prove that: :2^(n)C_(n)=(2^(n)[1.3.5(2n-1)])/(n!)

Statement-1: 1^(2)+2^(2)+....+n^(2)=(n(n+1)(2n+1))/(6)"for all "n in N Statement-2: 1+2+3....+n=(n(n+1))/(2),"for all"n in N