Question

\(\frac{1}{2003.2002}-\frac{1}{2002.2001}-........-\frac{1}{2.1}\)

Answer 1

\(\frac{1}{2003.2002}-\frac{1}{2002.2001}-...-\frac{1}{2.1}\)

\(=\frac{1}{2003.2002}-\left(\frac{1}{1.2}+\frac{1}{3.2}+...+\frac{1}{2001.2002}\right)\)

\(=\frac{1}{2003.2002}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2000}-\frac{1}{2001}+\frac{1}{2001}-\frac{1}{2002}\right)\)

\(=\frac{1}{2003.2002}-\left(1-\frac{1}{2002}\right)\)

\(=\frac{1}{2003.2002}-\frac{2001}{2002}\)