Sigma notation.

[Saldeat]

Hello,
I'm a first year computer science student and I have a question about sigma.
I'm given this series:

Now I don't understand something, if I wanna represent how the series looks from 1 to n should it look like this?


or this?


Thanks in advance

 

[Cubist]

Your first option (which was missing an equal sign) is correct because k is the variable that increments each term

[MATH]f_n=\sum_{k=1}^n\frac{n}{n^3+k^2}=\frac{n}{n^3+1^2}+\frac{n}{n^3+2^2}+\cdots+\frac{n}{n^3+n^2}[/MATH]

 

[Steven G]

Why would you think that both n and k changes?
n only changes, well when n changes. So what would f₂ equal?