# Math Help - Series Problem

1. ## Series Problem

Find ∑(x_i+i)^2 for i=5 to 168

x_i represents the 'i'th value in the list of x values.

I'm not really sure how to compute this. I'm worked with convergence tests and stuff for series, not familiar with solving this. More specifically, I don't understand what x_i represents in a way that I can plug it in and get a number for it.

2. ## Re: Series Problem

Just to clarify, your series is defined as;

You have a sequence of real numbers, $\{x_1,x_2,x_3,...\}$, and you want to compute the sum
$\displaystyle \sum_{i=5}^{168} (x_i+i)^2$

Do you have any more information on your numbers $x_n$?

3. ## Re: Series Problem

Correct. And no, I'm afraid that's all that was provided. I am perplexed.

4. ## Re: Series Problem

Well, I guess what you could do is;

$\displaystyle \sum_{i=5}^{168} (x_i+i)^2$ = $\displaystyle \sum_{i=5}^{168} x_i^2 + 2i x_i + i^2$ = $\displaystyle \sum_{i=5}^{168} x_i^2 +2\sum_{i=5}^{168} i x_i +\sum_{i=5}^{168} i^2$

Here you can at least get $\sum_{i=5}^{168} i^2$ with the formula given at Square pyramidal number - Wikipedia, the free encyclopedia, use it for n=168 and the substract n=5. For the other two, nothing comes to my mind as of yet without any precisions on the sequence $\{x_n\}$.