Question

Giusp mình vs ạ,mình cần gấp

Answer 1

\(M=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+...+\frac{3}{2021.2022}\)

    \(=3\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2021.2022}\right)\)

    \(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2021}-\frac{1}{2022}\right)\)

    \(=3\left(1-\frac{1}{2022}\right)\)

    \(=3.\frac{2021}{2022}\)

    \(=\frac{6063}{2022}\)