Question

Evaluate: lim(n tends to infinity) Summation over
r/(n^2+n+r) r is from 1 to n

Answer 1

\[\frac{1-4r-\pi r \sqrt{1-4r} \tan \left( \frac{1}{2} \pi \sqrt{1-4r}\right)}{-1+4r}\]

Answer 2

But the answer given is .5.Still could you explain your working.

Answer 3

Just to be clear, is this what you're asking?

Evaluate:
\[\underset{n\rightarrow\infty}{\lim}\sum_{r=1}^{n}\frac{r}{n^{2}+n+r}\]

Answer 4

yes

Answer 5

Hmmm, well, I'm going to have to think about that a while longer because I can't find any examples in my book, where you summing from r=1 up to some number "n", but both r and n are in the equation, which is why I wanted to be sure that's what you're really asking.