# Recursive Sequence Sum II

Algebra Level 4

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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