Prove by mathematical induction `1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)`

Prove by mathematical induction that, 1^(2)-2^(2)+3^(2)-4^(2)+ . . .. +(-1)^(n-1)*n^(2)=(-1)^(n-1)*(n(n+1))/(2),ninNN .

If ninNN , then by principle of mathematical induction prove that, 1^(2)+2^(2)+3^(2)+....+n^(2)gt(n^(3))/(3) .

For all ninNN , prove by principle of mathematical induction that, 1^(2)+3^(2)+5^(2)+ . . .+(2n-1)^(2)=(n)/(3)(4n^(2)-1) .

Prove by. mathematical induction : 1.2+2.2^2+3.2^3+...+n.2^n=(n-1)2^(n+1)+2,n in N

Prove by mathematical induction, n.1+(n-1).2+(n-2).3+…+2.(n-1)+1.n = (n(n+1)(n+2))/6 where n in N .

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)

By principle of mathematical induction,prove that 1^(3)+2^(3)+3^(3)+ . . .. +n^(3)=[(n(n+1))/(2)]^(2) for all ninNN

Prove by mathematical induction , 3^(2n+1)+2^(n+2) is divisible by 7, n in N

Prove by mathematical induction that, 2n+7lt(n+3)^(2) for all ninNN .

Applying the principle of mathematical induction (P.M.I.) prove that 1^2+2^2+3^2+.......+n^2=(n(n+1)(2n+1))/6