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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