Question

tính

A = \(\dfrac{1}{2.3.4}\) + \(\dfrac{1}{3.4.5}\) + \(\dfrac{1}{4.5.6}\) + \(\dfrac{1}{5.6.7}\) + \(\dfrac{1}{6.7.8}\) + \(\dfrac{1}{7.8.9}\) + \(\dfrac{1}{8.9.10}\)

Answer 1

\(A=\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+\dfrac{1}{4.5.6}+\dfrac{1}{5.6.7}+\dfrac{1}{6.7.8}+\dfrac{1}{7.8.9}+\dfrac{1}{8.9.10}\)

\(\Rightarrow2A=\dfrac{2}{2.3.4}+\dfrac{2}{3.4.5}+\dfrac{2}{4.5.6}+\dfrac{2}{5.6.7}+\dfrac{2}{6.7.8}+\dfrac{2}{7.8.9}+\dfrac{2}{8.9.10}\)

\(\Rightarrow2A=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{8.9}-\dfrac{1}{9.10}\)

\(\Rightarrow2A=\dfrac{1}{2.3}-\dfrac{1}{9.10}\)

\(\Rightarrow2A=\dfrac{22}{45}\)

\(\Rightarrow A=\dfrac{11}{45}\)