Recursive Sequence Sum II

Algebra Level 4

Let ana_n be a recursive function satisfying an=an11n(n1)a_n=a_{n-1}-\dfrac{1}{n(n-1)} for all positive integers n2n\geq 2, and a1=1a_1=1. What is the value of n=11000an \displaystyle \sum_{n=1} ^{1000} a_n? Round your answer to 5 decimal places.


Try Part I.

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