Question

tính

A = \(\frac{7}{10.11}+\frac{7}{11.12}+..................+\frac{7}{2016.2017}\)

Answer 1

\(A=\frac{7}{10.11}+\frac{7}{11.12}+...+\frac{7}{2016.2017}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{2016.2017}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{2016}-\frac{1}{2017}\)

\(\Rightarrow\frac{1}{7}A=\frac{1}{10}-\frac{1}{2017}=\frac{2017}{20170}-\frac{10}{20170}=\frac{2007}{20170}\)

\(\Rightarrow A=\frac{2007}{20170}\div\frac{1}{7}=\frac{14049}{20170}\)

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