Thread: How to simplify this sum

1. How to simplify this sum

$$\frac{k^2(k+1)^2}{4} + (k+1)^3$$

I am trying to simplify it down to

$$[\sum_{i=1}^{k+1} i]^2$$

Think I figured it out

$$(k+1)^2(\frac{k^2}{4} + (k+1)) = \frac{(k+1)^2(k^2+4k+4)}{4} = \frac{(k+1)^2(k+2)^2}{4} = [\frac{(k+1)(k+2)}{2}]^2 = [\sum_{i=1}^{k+1} i]^2]$$

2. Re: How to simplify this sum

That's correct