- #1

devinaxxx

## Homework Statement

i want to find limit value using riemann sum

[itex] \lim_{n\to\infty}\sum_{i = 1}^{2n} f(a+\frac{(b-a)k}{n})\cdot\frac{(b-a)}{n}= \int_a^b f(x)dx[/itex]<br>

question : <br>

[itex]\lim_{h \to \infty} =\frac{1}{2n+1}+\frac{1}{2n+3}+...+\frac{1}{2n+(2n-1)}[/itex]<br>

## Homework Equations

## The Attempt at a Solution

<br>

[itex]\lim_{h \to \infty}\sum_{k=1}^n \frac{1}{n}\frac{1}{2+(2k-1)\frac{1}{n}}[/itex]

i try to isolate 1/n but i can't find way to make this become [itex]f(\frac{k}{n})[/itex] since k is stuck in [itex]2k-1[/itex], can someone give me a hint? thanks