Question

Tính tổngn

C=3²/5×8+3²/8×11+...+3²/302×305

Answer 1

\(C=\dfrac{3^2}{5\cdot8}+\dfrac{3^2}{8\cdot11}+...+\dfrac{3^2}{302\cdot305}\)

\(=3\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{302\cdot305}\right)\)

\(=3\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{302}-\dfrac{1}{305}\right)\)

\(=3\left(\dfrac{1}{5}-\dfrac{1}{305}\right)=3\cdot\dfrac{60}{305}=\dfrac{180}{305}=\dfrac{36}{61}\)