Question

1/1.3+1/3.5+15.7+...+1/2011.2013

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Answer 1

Gọi  \(A=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2011.2013}\)

\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2011.2013}\)

\(\Rightarrow2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2011}-\frac{1}{2013}\)

\(\Rightarrow2A=1-\frac{1}{2013}\)

\(\Rightarrow2A=\frac{2012}{2013}\)

\(\Rightarrow A=\frac{1006}{2013}\)