# Thread: Stuck on Sigma Notation Problem

1. ## Stuck on Sigma Notation Problem

Hi guys. I've been viewing your website for a while now for guidance, but I haven't been able to solve this problem. Thus, I've registered to ask this question.

I've been putting off this homework until the end of spring break, and now I totally forgot how to do it. If anyone here knows how to do this problem, it'd be immensely appreciated if you could show me the steps to solve it.

Thank you!

2. Originally Posted by Rker
Hi guys. I've been viewing your website for a while now for guidance, but I haven't been able to solve this problem. Thus, I've registered to ask this question.

I've been putting off this homework until the end of spring break, and now I totally forgot how to do it. If anyone here knows how to do this problem, it'd be immensely appreciated if you could show me the steps to solve it.

Thank you!
Part 1:

Note that $\sum_{i=1}^n \left( 1 + \frac{2i}{n} \right) \left( \frac{2}{n}\right) = \frac{2}{n} \sum_{i=1}^n 1 + \left(\frac{2}{n}\right)^2 \sum_{i=1}^n i$.

$\sum_{i=1}^n i = \frac{n (n+1)}{2}$ and $\sum_{i=1}^n 1 = n$.

Substitute, simplify and then take the limit.

3. Dunno if you've covered Riemann sums but you can turn that one into an integral.

4. Originally Posted by Krizalid
Dunno if you've covered Riemann sums but you can turn that one into an integral.
I suspect (looking ahead to part 2) that the OP has to evaluate the integral using the Riemann sum rather than evaluate the Riemann sum using an integral. Of course, correctly evaluating the integral provides a check that the Riemann sum has been calculated correctly ....