Question

Tính

\(\dfrac{1}{99.97}-\dfrac{1}{97.95}-...-\dfrac{1}{3.1}\)

Answer 1

Đặt :

\(A=\dfrac{1}{99.97}-\dfrac{1}{97.95}-........-\dfrac{1}{3.1}\)

\(=\dfrac{1}{99.97}-\left(\dfrac{1}{97.95}+\dfrac{1}{95.93}+........+\dfrac{1}{3.1}\right)\)

\(=\dfrac{1}{99.97}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+.......+\dfrac{1}{95}-\dfrac{1}{97}\right)\)

\(=\dfrac{1}{99.97}-\dfrac{1}{2}\left(1-\dfrac{1}{97}\right)\)

\(=\dfrac{1}{99.97}-\dfrac{1}{2}.\dfrac{96}{97}\)

\(=-\dfrac{4751}{9603}\)