I’m doing a induction proof and need to find a way to prove (k(k+1)(k+2))/3 + k + 1 = ((k+1)(k+2)(k+3))/3. thanks

How can be the direction of rotation of an induction motor reversed apart from reversing the connections of condensor(capacitor in table fan) ?

Here is what I have done so far. Can anyone offer suggestions? 1^3 + 2^3 + 3^3 + * * * + n^3 = 1/4(n^2) Let P(1) = 1 then 1^3 = 1/4(1^2)=1 so P(1) is true. So we assume since it is true for P(1) then it must be true for P(k) as well and then need to prove true for P(k+1) so P(k) =...

I need help in figuring out how to prove 1+2n is less than or equal to 3^n by using induction.

I need to prove by induction that: 1/(1x3) + 1/(2x4) +... + 1/n(n+2) = n(3n+5)/4(n+1)(n+2) Thanks