A. 1 / 1 x 2 + 1 / 2 x 3 + 1 / 3 x 4 + …. + 1 / 2019 x 2020

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A. 1 / 1 x 2 + 1 / 2 x 3 + 1 / 3 x 4 + …. + 1 / 2019 x 2020

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  1.    $\dfrac{1}{1 × 2}$ + $\dfrac{1}{2 × 3}$ + …. + $\dfrac{1}{2019 × 2020}$

    $\text{= 1 – $\dfrac{1}{2}$ + $\dfrac{1}{2}$ – $\dfrac{1}{2}$ + … – $\dfrac{1}{2020}$}$

    $\text{= 1 – $\dfrac{1}{2020}$}$

    $\text{= $\dfrac{2019}{2020}$}$

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  2. A=$\frac{1}{1×2}$+$\frac{1}{2×3}$+$\frac{1}{3×4}$+…..+$\frac{1}{2019×2020}$ 

    A=1-$\frac{1}{2}$+$\frac{1}{2}$-$\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{4}$+……+$\frac{1}{2019}$- $\frac{1}{2020}$ 

    A=1-$\frac{1}{2020}$=$\frac{2019}{2020}$ 

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