Prove by the principle of mathematical induction that for all `n in N :` `1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)`

Prove by the principle of mathematical induction that for all n in N:1^(2)+2^(2)+3^(2)+...+n^(2)=(1)/(6)n(n+1)(2n+1)

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by the principle of mathematical induction that for all n in N:1+4+7+...+(3n-2)=(1)/(2)n(3n-1)

Prove the following by using the principle of mathematical induction for all n in N :- 1^2+3^2+5^2 + ...+(2n-1)^2=(n(2n-1)(2n+1))/3 .

Prove the following by using the principle of mathematical induction for all n in N 1^2 +3 ^2 + 5^2 +………..+ (2n-1)^2 = (n(2n - 1)(2n+1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1^(2)+3^(2)+5^(2)+...(2n-1)^(2)= (n(2n-1)(2n+1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1^(2)+3^(2)+5^(2)+...(2n-1)^(2)= (n(2n-1)(2n+1))/(3)

Prove that by using the principle of mathematical induction for all n in N : 1^(2)+3^(2)+5^(2)+...(2n-1)^(2)= (n(2n-1)(2n+1))/(3)

Prove that 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)

Prove that 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)