Question

Tính tổng M=3/2.4+3/4.6+3/6.8+....+3/100.102

Answer 1

\(M=\dfrac{3}{2.4}+\dfrac{3}{4.6}+\dfrac{3}{6.8}+...+\dfrac{3}{100.102}\)

=> \(2M=\dfrac{3.2}{2.4}+\dfrac{3.2}{4.6}+\dfrac{3.2}{6.8}+...+\dfrac{3.2}{100.102}\)

=> \(2M=3.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{100.102}\right)\)

=> \(2M=3.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{100}-\dfrac{1}{102}\right)\)

=> \(2M=3.\left(\dfrac{1}{2}-\dfrac{1}{102}\right)\)

=> \(2M=3.\dfrac{25}{51}\)

=> \(2M=\dfrac{25}{17}\)

=> \(M=\dfrac{25}{17}:2\)

=> \(M=\dfrac{25}{34}\)