Tính tổng S=1/1.3+1/3.5+1/5.7+…+1/99.101

Đáp án:

Giải thích các bước giải:

\(\begin{array}{l}S = 1/1.3 + 1/3.5 + 1/5.7 + … + 1/99.1011\\S = \frac{1}{{1.3}} + \frac{1}{{3.5}} + \frac{1}{{5.7}} + … + \frac{1}{{99.101}}\\ = \frac{1}{2}.\left( {1 – \frac{1}{3} + \frac{1}{3} – \frac{1}{5} + \frac{1}{5} – \frac{1}{7} + … + \frac{1}{{99}} – \frac{1}{{101}}} \right)\\ = \frac{1}{2}.\left( {1 – \frac{1}{{101}}} \right)\\ = \frac{1}{2}.\frac{{100}}{{101}}\\ = \frac{{50}}{{101}}\end{array}\)