50 50/3 25/3 20/4 ... 100/98.99 1/99

Lời giải:

\(\begin{array}{l}50 + \frac{{50}}{3} + \frac{{25}}{3} + \frac{{20}}{4} + .... + \frac{{100}}{{98.99}} + \frac{1}{{99}}\\ = \frac{{100}}{{1.2}} + \frac{{100}}{{2.3}} + \frac{{100}}{{3.4}} + \frac{{100}}{{4.5}} + ... + \frac{{100}}{{98.99}} + \frac{{100}}{{99.100}}\\ = 100.\left( {1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{{99}} - \frac{1}{{100}}} \right)\\ = 100.\left( {1 - \frac{1}{{100}}} \right)\\ = 100 - 1 = 99\end{array}\)