Question

Use mathematical induction to show that this statement is true. I will draw a diagram. I appreciate any help!

Answer 1

\[\sum_{i=1}^{n}i^3 = [n(n+1)/2]^2\]

Answer 2

Does it work for n = 1?

Answer 3

I do believe it does. I got that it does. I am not sure how to prove the second part where you have to prove if it is k+1 which is the second half of mathematical induction

Answer 4

You believe? Does it or doesn't it?

Answer 5

It does

Answer 6

Perfect. Proceed with confidence.

If it works for a value, k, we have: \(\sum\limits_{i=1}^{k} i^{3} = \left(\dfrac{k(k+1)}{2}\right)^{2}\).

Can we use this fact to demonstrate that: \(\sum\limits_{i=1}^{k} i^{3} + (k+1)^{3} = \left(\dfrac{(k+1)(k+2)}{2}\right)^{2}\)

Answer 7

Yes we can. That makes sense. The k+1 always throws me off. Thank you for the motivation on confidence. The class I am has really lowered it. Now all I need to do is factor the second equation our farther and it should be perfect

Answer 8

It's a little bit of algebra. You can do this!

Answer 9

I pretty sure I got it! My equations matched!