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 $\displaystyle a_{n}=3n+2$ , is the restriction to the integers of a polynomial function $\displaystyle y=f(x)$. Construct the partial sums of such series and use them to identify the function $\displaystyle f(x)$.

I started by writing the series in sigma notation,

$\displaystyle \sum_{i=1}^n (3i+2)$

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

$\displaystyle \sum_{i=1}^n (3i+2)$

$\displaystyle

=\sum_{i=1}^n (3i) + \sum_{i=1}^n (2)$

$\displaystyle =3 \sum_{i=1}^n (i) + 2$

Right?

I want to say that $\displaystyle f(x)=3x+2$ which makes sense as it would be $\displaystyle a_{n}=3n+2$ if restricted to the integers, but I'm not sure if I've found my correct partial sum?

Thanks for your time!