Question

f) \(-\dfrac{1}{30}-\dfrac{1}{15.13}-\dfrac{1}{13.11}-...-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)

Answer 1

\(-\dfrac{1}{30}-\dfrac{1}{15.13}-\dfrac{1}{13.11}-...-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)

Đặt \(A=-\dfrac{1}{30}-\dfrac{1}{15.13}-\dfrac{1}{13.11}-...-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)

\(\Rightarrow2A=-\dfrac{1}{15}-\left(\dfrac{2}{15.13}+\dfrac{2}{13.11}+...+\dfrac{2}{5.3}+\dfrac{2}{3.1}\right)\)

\(\Rightarrow2A=-\dfrac{1}{15}-\left(\dfrac{1}{15}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{11}+...+\dfrac{1}{5}-\dfrac{1}{3}+\dfrac{1}{3}-1\right)\)

\(\Rightarrow2A=-\dfrac{1}{15}-\left(\dfrac{1}{15}-1\right)=-\dfrac{1}{15}-\dfrac{1}{15}+1\)

\(=\dfrac{13}{15}\)

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