Question

Thực hiện phép tính:

A=3.1/1.2−5.1/2.3+7.1/3.4−...+15.1/7.8−17.1/8.9

Answer 1

Dạng tổng quát: \(\dfrac{a+b}{ab}=\dfrac{1}{a}+\dfrac{1}{b}\)

Áp dụng:

\(A=\dfrac{3}{1.2}-\dfrac{5}{2.3}+\dfrac{7}{3.4}-...+\dfrac{15}{7.8}-\dfrac{17}{8.9}\)

\(=\left(1+\dfrac{1}{2}\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}\right)+\left(\dfrac{1}{3}+\dfrac{1}{4}\right)-...+\left(\dfrac{1}{7}+\dfrac{1}{8}\right)-\left(\dfrac{1}{8}+\dfrac{1}{9}\right)\)

\(=1+\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{4}-...+\dfrac{1}{7}+\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{9}\)

\(1-\dfrac{1}{9}=\dfrac{8}{9}\)