Thread: Proof of summation of i^3 by induction, help needed

1. Proof of summation of i^3 by induction, help needed

This is my first proof using induction and, as expected, I'm stuck. In fact, I don't know where to start. Any help is appreciated. THanks.

2. Originally Posted by qtpipi

This is my first proof using induction and, as expected, I'm stuck. In fact, I don't know where to start. Any help is appreciated. THanks.
Start with the base case, when $n=1$ is it true?

Then the induction step is to assume it true for $n=k$, and show that implies that it is true when $n=k+1$.

So you need to show that the assumption that:

$\sum_{i=1}^ki^3=\left(\frac{k(k+1)}{2} \right)^2$

implies that:

$\sum_{i=1}^{k+1}i^3 = \left(\sum_{i=1}^ki^3\right) + (k+1)^3=\left(\frac{(k+1)(k+2)}{2} \right)^2$

CB