Trang chủ » Hỏi đáp » Môn Toán tính nhanh:3/4×6+3/6×8+3/8×10+…..+3/2018×2020 11/10/2023 tính nhanh:3/4×6+3/6×8+3/8×10+…..+3/2018×2020
Giải đáp: $\dfrac{{189}}{{505}}$ Lời giải và giải thích chi tiết: $\begin{array}{l}\dfrac{3}{{4 \times 6}} + \dfrac{3}{{6 \times 8}} + \dfrac{3}{{8 \times 10}} + … + \dfrac{3}{{2018 \times 2020}}\\ = \dfrac{3}{2} \times \left( {\dfrac{2}{{4 \times 6}} + \dfrac{2}{{6 \times 8}} + \dfrac{2}{{8 \times 10}} + … + \dfrac{2}{{2018 \times 2020}}} \right)\\ = \dfrac{3}{2} \times \left( {\dfrac{{6 – 4}}{{4 \times 6}} + \dfrac{{8 – 6}}{{6 \times 8}} + \dfrac{{10 – 8}}{{8 \times 10}} + … + \dfrac{{2020 – 2018}}{{2018 \times 2020}}} \right)\\ = \dfrac{3}{2} \times \left( {\dfrac{1}{4} – \dfrac{1}{6} + \dfrac{1}{6} – \dfrac{1}{8} + …. + \dfrac{1}{{2018}} – \dfrac{1}{{2020}}} \right)\\ = \dfrac{3}{2} \times \left( {\dfrac{1}{4} – \dfrac{1}{{2020}}} \right)\\ = \dfrac{3}{2} \times \dfrac{{504}}{{2020}}\\ = \dfrac{{3 \times 252}}{{2020}}\\ = \dfrac{{3 \times 63}}{{505}} = \dfrac{{189}}{{505}}\end{array}$ Trả lời
\dfrac{3}{{4 \times 6}} + \dfrac{3}{{6 \times 8}} + \dfrac{3}{{8 \times 10}} + … + \dfrac{3}{{2018 \times 2020}}\\
= \dfrac{3}{2} \times \left( {\dfrac{2}{{4 \times 6}} + \dfrac{2}{{6 \times 8}} + \dfrac{2}{{8 \times 10}} + … + \dfrac{2}{{2018 \times 2020}}} \right)\\
= \dfrac{3}{2} \times \left( {\dfrac{{6 – 4}}{{4 \times 6}} + \dfrac{{8 – 6}}{{6 \times 8}} + \dfrac{{10 – 8}}{{8 \times 10}} + … + \dfrac{{2020 – 2018}}{{2018 \times 2020}}} \right)\\
= \dfrac{3}{2} \times \left( {\dfrac{1}{4} – \dfrac{1}{6} + \dfrac{1}{6} – \dfrac{1}{8} + …. + \dfrac{1}{{2018}} – \dfrac{1}{{2020}}} \right)\\
= \dfrac{3}{2} \times \left( {\dfrac{1}{4} – \dfrac{1}{{2020}}} \right)\\
= \dfrac{3}{2} \times \dfrac{{504}}{{2020}}\\
= \dfrac{{3 \times 252}}{{2020}}\\
= \dfrac{{3 \times 63}}{{505}} = \dfrac{{189}}{{505}}
\end{array}$