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    OlympiadMediumAlgebra7–9

    A Sum That Collapses

    Uma Soma que Colapsa

    Find the value of 11×2+12×3+13×4+⋯+199×100\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \cdots + \frac{1}{99 \times 100}.

    Write a single term as a difference of two simpler fractions and then look down the whole list.

    Solution

    Step 1 of 7

    1. 1.For each kk,