Giá trị của \(A = \left( {\frac{3}{{1.8}} + \frac{3}{{8.15}} + \frac{3}{{15.22}} + \ldots + \frac{3}{{106.113}}} \right) - \left( {\frac{{25}}{{50.55}} + \frac{{25}}{{55.60}} + \ldots + \frac{{25}}{{95.100}}} \right)\) là
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Lời giải:
Báo sai\(\begin{array}{l} A = \left( {\frac{3}{{1.8}} + \frac{3}{{8.15}} + \frac{3}{{15.22}} + \ldots + \frac{3}{{106.113}}} \right) - \left( {\frac{{25}}{{50.55}} + \frac{{25}}{{55.60}} + \ldots + \frac{{25}}{{95.100}}} \right)\\ Đặt\,B = \frac{3}{{1.8}} + \frac{3}{{8.15}} + \frac{3}{{15.22}} + \ldots + \frac{3}{{106.113}} \Rightarrow 7B = 3\left( {\frac{7}{{1.8}} + \frac{7}{{8.15}} + \frac{7}{{15.22}} + \ldots + \frac{7}{{106.113}}} \right)\\ \Rightarrow 7B = 3\left( {\frac{1}{1} - \frac{1}{8} + \frac{1}{8} - \frac{1}{{15}} + \frac{1}{{15}} - \frac{1}{{22}} + \ldots + \frac{1}{{106}} - \frac{1}{{113}}} \right) = 3\left( {1 - \frac{1}{{113}}} \right) = 3 \cdot \frac{{112}}{{113}} \Rightarrow B = \frac{{3.112}}{{7.113}} = \frac{{48}}{{113}}\\ và\,\,\,\,C = \frac{{25}}{{50.55}} + \frac{{25}}{{55.60}} + \ldots + \frac{{25}}{{95.100}} \Rightarrow 5C = \frac{5}{{50.55}} + \frac{5}{{55.60}} + \ldots + \frac{5}{{95.100}}\\ \Rightarrow 5C = \frac{1}{{50}} - \frac{1}{{100}} = \frac{1}{{100}} \Leftrightarrow C = \frac{1}{{500}}\\ \text{Khi đó }A = B - C = \frac{{48}}{{113}} - \frac{1}{{500}} \end{array}\)
