Đáp án:
$\rm M=\dfrac{8}{9}$
Giải thích các bước giải:
$\rm M=\dfrac{3}{2}-\dfrac{5}{6}+\dfrac{7}{12}-\dfrac{9}{20}+\dfrac{11}{30}-\dfrac{13}{42}+\dfrac{15}{56}-\dfrac{17}{72}\\\Rightarrow\rm M=\dfrac{3}{1.2}-\dfrac{5}{2.3}+\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}\\\Rightarrow\rm M=\dfrac{2+1}{1.2}-\dfrac{3+2}{2.3}+\dfrac{4+3}{3.4}-\dfrac{5+4}{4.5}+\dfrac{6+5}{5.6}-\dfrac{7+6}{6.7}+\dfrac{8+7}{7.8}-\dfrac{9+8}{8.9}\\\Rightarrow\rm M=\left(1+\dfrac{1}{2}\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}\right)+\left(\dfrac{1}{3}+\dfrac{1}{4}\right)-\left(\dfrac{1}{4}+\dfrac{1}{5}\right)+\left(\dfrac{1}{5}+\dfrac{1}{6}\right)-\left(\dfrac{1}{6}+\dfrac{1}{7}\right)+\left(\dfrac{1}{7}+\dfrac{1}{8}\right)-\left(\dfrac{1}{8}+\dfrac{1}{9}\right)\\\rm M=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{9}\\\Rightarrow\rm M=1-\dfrac{1}{9}\\\Rightarrow\rm M=\dfrac{8}{9}$
Vậy $\rm M=\dfrac{8}{9}$.
