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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

Find the value of

$$\lim_{n\rightarrow \infty} \sum_{r=0}^n \left(\frac{1}{4r+1}-\frac{1}{4r+3}\right)$$

**Attempt:**

I tried writing down a few terms to see if the terms cancel but no luck there. I couldn't find any closed form for the summation.

Next, I thought of converting it into a definite integral. The usual approach is to consider $r/n$ as $x$ and $1/n$ as dx but I am unable to find a way to do this.

I am completely clueless now.

Any help is appreciated. Thanks!

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