. tính 1/1.1985 1/2 .1986

Lời giải:

F = \(\frac{1}{{1.1985}} + \frac{1}{{2.1986}} + \frac{1}{{3.1987}} + ... + \frac{1}{{16.2000}}\)

\(\begin{array}{l}1984F = \frac{{1984}}{{1.1985}} + \frac{{1984}}{{2.1986}} + \frac{{1984}}{{3.1987}} + ... + \frac{{1984}}{{16.2000}}\\1984F = \left( {1 - \frac{1}{{1985}}} \right) + \left( {\frac{1}{2} - \frac{1}{{1986}}} \right) + \left( {\frac{1}{3} - \frac{1}{{1987}}} \right) + ... + \left( {\frac{1}{{16}} - \frac{1}{{2000}}} \right)\\1984F = \left( {1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{16}}} \right) - \left( {\frac{1}{{1985}} + \frac{1}{{1986}} + \frac{1}{{1987}} + ... + \frac{1}{{2000}}} \right)\\F = \frac{{\left( {1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{{16}}} \right) - \left( {\frac{1}{{1985}} + \frac{1}{{1986}} + \frac{1}{{1987}} + ... + \frac{1}{{2000}}} \right)}}{{1984}}\end{array}\)