Question

Tính tổng : A=\(\dfrac{2010}{2}+\dfrac{2010}{6}+\dfrac{2010}{12}+.....+\dfrac{2010}{9900}\)

Answer 1

\(A=\dfrac{2010}{2}+\dfrac{2010}{6}+\dfrac{2010}{12}+...+\dfrac{2010}{9900}=2010\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\right)=2010\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)=2010\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)=2010\left(1-\dfrac{1}{100}\right)=2010.\dfrac{99}{100}=\dfrac{19899}{10}\)