- #1

songoku

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- Homework Statement
- Show that:

$$\sum_{r=1}^n \frac{1}{n} \left(1+\frac{r}{n} \right)^{-1}\approx \int_0^1 (1+x)^{-1} dx$$

- Relevant Equations
- Not sure

Writing down several terms of the summation and then doing some simplifying, I get:

$$\sum_{r=1}^n \frac{1}{n} \left(1+\frac{r}{n} \right)^{-1}= \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+...\frac{1}{2n}$$

How to change this into integral form? Thanks

$$\sum_{r=1}^n \frac{1}{n} \left(1+\frac{r}{n} \right)^{-1}= \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+...\frac{1}{2n}$$

How to change this into integral form? Thanks