Question

Tính : B=5/10×11+5/11×12+5/12×13+...+5/19×20

Answer 1

\(B=\dfrac{5}{10.11}+\dfrac{5}{11.12}+\dfrac{5}{12.13}+...+\dfrac{5}{19.20}\)

\(\Rightarrow\dfrac{B}{5}=\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{19.20}\)

\(=\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=\dfrac{1}{10}-\dfrac{1}{20}=\dfrac{2}{20}-\dfrac{1}{20}=\dfrac{1}{20}\)

\(\Rightarrow B=\dfrac{1}{20}.5=\dfrac{5}{20}=\dfrac{1}{4}\)