Question

Answer 1

Có: \(B=\dfrac{1}{9.10}-\dfrac{1}{8.9}-...-\dfrac{1}{2.3}-\dfrac{1}{1.2}\)

\(\Rightarrow B=\dfrac{1}{9.10}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\right)\)

\(\Rightarrow B=\dfrac{1}{9.10}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)

\(\Rightarrow B=\dfrac{1}{9.10}-\left(1-\dfrac{1}{9}\right)\)

\(\Rightarrow B=\dfrac{1}{90}-\dfrac{80}{90}=-\dfrac{79}{90}\)