2 câu trả lời
Đáp án:
$\dfrac{50}{101}$
Giải thích các bước giải:
\(\begin{array}{l}S = \dfrac{1}{1.3} + \dfrac{1}{3.5} + \dfrac{1}{5.7} + ... + \dfrac{1}{99.1011}\\S = \dfrac{1}{{1.3}} + \dfrac{1}{{3.5}} + \dfrac{1}{{5.7}} + ... + \dfrac{1}{{99.101}}\\ = \dfrac{1}{2}.\left( {1 - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + ... + \dfrac{1}{{99}} - \dfrac{1}{{101}}} \right)\\ = \dfrac{1}{2}.\left( {1 - \dfrac{1}{{101}}} \right)\\ = \frac{1}{2}.\dfrac{{100}}{{101}}\\ = \dfrac{{50}}{{101}}\end{array}\)
S=1/1.3+1/3.5+1/5.7+...+1/99.101
2S= 2/1.3+2/3.5+2./5.7+...+2/99.101
= 1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101
= 1-1/101
= 100/101
=> S= 100/101: 2 = 50/101
