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Let $a_n$ be a recursive function satisfying $a_n=a_{n-1}-\dfrac{1}{n(n-1)}$ for all positive integers $n\geq 2$, and $a_1=1$. What is the value of $\displaystyle \sum_{n=1} ^{1000} a_n$? $$Round your answer to 5 decimal places.

Try Part I.

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