Question

Tính:

\(-1-\dfrac{1}{3}-\dfrac{1}{6}-\dfrac{1}{10}-\dfrac{1}{15}-...-\dfrac{1}{1225}\)

Answer 1

\(-1-\dfrac{1}{3}-\dfrac{1}{6}-...-\dfrac{1}{1225}\)

\(=\dfrac{-1}{2}\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2450}\right)\)

\(=\dfrac{-1}{2}\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)\)

\(=\dfrac{-1}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)

\(=\dfrac{-1}{2}\left(1-\dfrac{1}{50}\right)\)

\(=\dfrac{-1}{2}.\dfrac{49}{50}=\dfrac{-49}{100}\)

Vậy...