Đáp án: $M=\dfrac{33}{50}$
Giải thích các bước giải:
Ta có:
$M=\dfrac1{1.2}+\dfrac1{2.7}+\dfrac1{7.5}+\dfrac1{5.13}+...+\dfrac1{50.97}$
$\to \dfrac12M=\dfrac1{2.1.2}+\dfrac1{2.2.7}+\dfrac1{2.7.5}+\dfrac1{2.5.13}+...+\dfrac1{2.50.97}$
$\to \dfrac12M=\dfrac1{1.4}+\dfrac1{4.7}+\dfrac1{7.10}+\dfrac1{10.13}+...+\dfrac1{97.100}$
$\to \dfrac32M=\dfrac{3}{1.4}+\dfrac3{4.7}+\dfrac3{7.10}+\dfrac3{10.13}+...+\dfrac3{97.100}$
$\to \dfrac32M=\dfrac{4-1}{1.4}+\dfrac{7-4}{4.7}+\dfrac{10-7}{7.10}+\dfrac{13-10}{10.13}+...+\dfrac{100-97}{97.100}$
$\to\dfrac32M=\dfrac11-\dfrac14+\dfrac14-\dfrac17+\dfrac17-\dfrac1{10}+\dfrac1{10}-\dfrac1{13}+...+\dfrac1{97}-\dfrac1{100}$
$\to \dfrac32M=1-\dfrac1{100}$
$\to\dfrac32M=\dfrac{99}{100}$
$\to M=\dfrac{33}{50}$
