Hey folks, been an awful long time since I've been working with series, could definitely use a push with this problem.

The series obtained from the sequence

, is the restriction to the integers of a polynomial function

. Construct the partial sums of such series and use them to identify the function

.

I started by writing the series in sigma notation,

And to construct the partial sums, we can split up the total sum into:

Right?

I want to say that

which makes sense as it would be

if restricted to the integers, but I'm not sure if I've found my correct partial sum?

Thanks for your time!