tính nhanh:3/4×6+3/6×8+3/8×10+…..+3/2018×2020

2 bình luận về “tính nhanh:3/4×6+3/6×8+3/8×10+…..+3/2018×2020”

1. Giải đáp: ${\displaystyle \frac{189}{505}}$

    

   Lời giải và giải thích chi tiết:

   $\begin{array}{l}{\displaystyle \frac{3}{4\times 6}}+{\displaystyle \frac{3}{6\times 8}}+{\displaystyle \frac{3}{8\times 10}}+\dots +{\displaystyle \frac{3}{2018\times 2020}}\\ ={\displaystyle \frac{3}{2}}\times \left({\displaystyle \frac{2}{4\times 6}}+{\displaystyle \frac{2}{6\times 8}}+{\displaystyle \frac{2}{8\times 10}}+\dots +{\displaystyle \frac{2}{2018\times 2020}}\right)\\ ={\displaystyle \frac{3}{2}}\times \left({\displaystyle \frac{6–4}{4\times 6}}+{\displaystyle \frac{8–6}{6\times 8}}+{\displaystyle \frac{10–8}{8\times 10}}+\dots +{\displaystyle \frac{2020–2018}{2018\times 2020}}\right)\\ ={\displaystyle \frac{3}{2}}\times \left({\displaystyle \frac{1}{4}}–{\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{6}}–{\displaystyle \frac{1}{8}}+\dots .+{\displaystyle \frac{1}{2018}}–{\displaystyle \frac{1}{2020}}\right)\\ ={\displaystyle \frac{3}{2}}\times \left({\displaystyle \frac{1}{4}}–{\displaystyle \frac{1}{2020}}\right)\\ ={\displaystyle \frac{3}{2}}\times {\displaystyle \frac{504}{2020}}\\ ={\displaystyle \frac{3\times 252}{2020}}\\ ={\displaystyle \frac{3\times 63}{505}}={\displaystyle \frac{189}{505}}\end{array}$

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