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

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 .

Prove by mathematical induction 1/1.2 + 1/2.3 + . . .+ 1/((n)(n+1)) =n/((n+1))

Prove by mathematical induction that 1^3+2^3+……+n^3=[(n(n+1))/2]^2

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

Using the principle of mathematical induction,prove that :.2.3+2.3.4+...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4) for all n in N

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