Question

[Thuỳ Anh Lâm]

B=\(\dfrac{5}{2^2.3^2}\)+\(\dfrac{7}{3^2.4^2}\)+...+\(\dfrac{19}{\text{9}^{\text{2}}.10^2}\)

Tính nhanh

Answer 1

[Trịnh Bảo Duy An]

\(B=\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)
\(B=\dfrac{1}{4}-\dfrac{1}{100}=\dfrac{6}{25}\)