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 that 1^3+2^3+……+n^3=[(n(n+1))/2]^2

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

By mathematical induction prove that, 1*2+2*2^(2)+3*2^(3)+ . . .+n*2^(n)=(n-1)*2^(n+1)+2,ninNN .

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 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)

For all ninNN , prove by principle of mathematical induction that, (1)/(2)+(1)/(4)+(1)/(8)+ . . .+(1)/(2^(n))=1-(1)/(2^(n)) .

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