Evaluate `sum_(n=1)^(1000)int_(n-1)^(n)|cos2pix|dx`

Explanation

To evaluate the expression \( \sum_{n=1}^{1000} \int_{n-1}^{n} |\cos(2\pi x)| \, dx \), we can break it down step by step.

### Step 1: Rewrite the Summation and Integral
We start by rewriting the sum and integral:
\[ \sum_{n=1}^{1000} \int_{n-1}^{n} |\cos(2\pi x)| \, dx \]
This can be expressed as a single integral over the interval from 0 to 1000:
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