Cho \(A = \frac{4}{{7.31}} + \frac{6}{{7.41}} + \frac{9}{{10.41}} + \frac{7}{{10.57}};\,\,B = \frac{7}{{19.31}} + \frac{5}{{19.43}} + \frac{3}{{23.43}} + \frac{{11}}{{23.57}}\). Tính \( \frac{A}{B}\)
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Lời giải:
Báo saiTa có
\(\begin{array}{l} A = \frac{4}{{7.31}} + \frac{6}{{7.41}} + \frac{9}{{10.41}} + \frac{7}{{10.57}}\\ \Rightarrow \frac{A}{5} = \frac{4}{{31.35}} + \frac{6}{{35.41}} + \frac{9}{{41.50}} + \frac{7}{{50.57}} = \left( {\frac{1}{{31}} - \frac{1}{{35}}} \right) + \left( {\frac{1}{{35}} - \frac{1}{{41}}} \right) + \left( {\frac{1}{{41}} - \frac{1}{{50}}} \right) + \left( {\frac{1}{{50}} - \frac{1}{{57}}} \right) = \frac{1}{{31}} - \frac{1}{{57}}\\ B = \frac{7}{{19.31}} + \frac{5}{{19.43}} + \frac{3}{{23.43}} + \frac{{11}}{{23.57}}\\ \Rightarrow \frac{B}{2} = \frac{7}{{31.38}} + \frac{5}{{38.43}} + \frac{3}{{43.46}} + \frac{{11}}{{46.57}} = \left( {\frac{1}{{31}} - \frac{1}{{38}}} \right) + \left( {\frac{1}{{38}} - \frac{1}{{43}}} \right) + \left( {\frac{1}{{43}} - \frac{1}{{46}}} \right) + \left( {\frac{1}{{46}} - \frac{1}{{57}}} \right) = \frac{1}{{31}} - \frac{1}{{57}}\\ \frac{A}{5} = \frac{B}{2} \Rightarrow \frac{A}{B} = \frac{5}{2} \end{array}\)
