Question

c = 1/4x7 + 1/7x10 + 1/10x13 +...+1/2020x2023

giải chi tiết + Đúng

Answer 1

\(C=\dfrac{1}{4.7}+\dfrac{1}{7.10}+\dfrac{1}{10.13}+...+\dfrac{1}{2020+2023}\)

\(=\dfrac{1}{3}\left(\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{2020.2023}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{2020}-\dfrac{1}{2023}\right)\)

\(=\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{2023}\right)\)

\(=\dfrac{1}{3}.\dfrac{2019}{8092}\)

\(=\dfrac{673}{8092}\)