Question

Tính:

1 / 2003.2004 - 1 / 2002.2003 - . . . - 1 / 3.2 - 1 / 2.1

Answer 1

Đặt \(A=\frac{1}{2003.2004}-\frac{1}{2002.2003}-...-\frac{1}{3.2}-\frac{1}{2.1}\)

\(\Rightarrow-A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2002.2003}+\frac{1}{2003.2004}\)

\(\Rightarrow-A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2002}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}\)

\(\Rightarrow-A=1-\frac{1}{2004}\)

\(\Rightarrow-A=\frac{2003}{2004}\)

\(\Rightarrow A=\frac{-2003}{2004}\)