Question

Tính nhanh:

      \(\frac{-1}{22003.2002}-\frac{1}{2002-2001}-\frac{1}{2001-2000}-......-\frac{1}{3.2}-\frac{1}{2.1}\)

Answer 1

\(-\frac{1}{2003.2002}-\frac{1}{2002.2001}-....-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2002.2003}\right)\)

\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2002}-\frac{1}{2003}\right)\)

\(=-\left(1-\frac{1}{2003}\right)\)

\(=\frac{-2002}{2003}\)

Answer 2

\(\frac{-1}{2003.2002}-\frac{1}{2002.2001}-\frac{1}{2001.2000}-....-\frac{1}{3.2}-\frac{1}{2.1}\)

\(=-\left(\frac{1}{2003.2002}+\frac{1}{2002.2001}+\frac{1}{2001.2000}+....+\frac{1}{3.2}+\frac{1}{2.1}\right)\)

\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{2000.2001}+\frac{1}{2001.2002}+\frac{1}{2002.2003}\right)\)

\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{2001}-\frac{1}{2002}+\frac{1}{2002}-\frac{1}{2003}\right)\)
\(=-\left(1-\frac{1}{2003}\right)\)

\(=-\frac{2002}{2003}\)

Answer 3

-2002/2003

Answer 4

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