Câu hỏi:
Cho \[M = \frac{{17}}{5}.\frac{{ – 31}}{{125}}.\frac{1}{2}.\frac{{10}}{{17}}.{\left( {\frac{{ – 1}}{2}} \right)^3}\] và \[N = \left( {\frac{{17}}{{28}} + \frac{{28}}{{29}} – \frac{{19}}{{30}} – \frac{{20}}{{31}}} \right).\left( {\frac{{ – 5}}{{12}} + \frac{1}{4} + \frac{1}{6}} \right)\] . Khi đó tổng M + N bằng
A. \[\frac{{ – 62}}{{125}}\]
B. \[\frac{{31}}{{1000}}\]
Đáp án chính xác
C. \[\frac{{ – 31}}{{100}}\]
D. \[\frac{{31}}{{100}}\]
Trả lời:
\[M = \frac{{17}}{5}.\frac{{ – 31}}{{125}}.\frac{1}{2}.\frac{{10}}{{17}}.{\left( {\frac{{ – 1}}{2}} \right)^3}\]
\[M = \frac{{17.\left( { – 31} \right).1.10.{{\left( { – 1} \right)}^3}}}{{{{5.125.2.17.2}^3}}}\]
\[M = \frac{{ – 31.\left( { – 1} \right)}}{{{{125.2}^3}}}\]
\[M = \frac{{31}}{{1000}}\]
\[N = \left( {\frac{{17}}{{28}} + \frac{{28}}{{29}} – \frac{{19}}{{30}} – \frac{{20}}{{31}}} \right).\left( {\frac{{ – 5}}{{12}} + \frac{1}{4} + \frac{1}{6}} \right)\]
\[N = \left( {\frac{{17}}{{28}} + \frac{{28}}{{29}} – \frac{{19}}{{30}} – \frac{{20}}{{31}}} \right).\left( {\frac{{ – 5}}{{12}} + \frac{3}{{12}} + \frac{2}{{12}}} \right)\]
\[N = \left( {\frac{{17}}{{28}} + \frac{{28}}{{29}} – \frac{{19}}{{30}} – \frac{{20}}{{31}}} \right).0\]
N = 0
Vậy \[M + N = \frac{{31}}{{1000}} + 0 = \frac{{31}}{{1000}}\]
Đáp án cần chọn là: B
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