Tính nhanh : P=1/1×2+1/2×3+1/3×4+…..+1/2018×2019

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1. $P = \dfrac{1}{1 \times 2} + \dfrac{1}{2 \times 3} + \dfrac{1}{3 \times 4} + …. + \dfrac{1}{2018 \times 2019}$

   $P =\dfrac{1}{1} – \dfrac{1}{2} + \dfrac{1}{2} -\dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + … + \dfrac{1}{2018} -\dfrac{1}{2019}$

   $P = 1 – \dfrac{1}{2019}$

   $P = \dfrac{2018}{2019}$

    

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2. Đáp án:

   $P=\frac{1}{1×2}+\frac{1}{2×3}+\frac{1}{3×4}+\frac{1}{2018×2019}$

   $⇔P=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{2018}-\frac{1}{2019}$

   $⇔P=1-\frac{1}{2019}=\frac{2018}{2019}$

   #NOCOPY

    

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