by Tính \(5 – \frac{1}{2} – \frac{5}{6} – \frac{{11}}{{12}} – \frac{{19}}{{20}} – \frac{{29}}{{30}}\)
A. \(\frac{1}{6}\)
B. \(\frac{5}{6}\)
C. \(\frac{{11}}{{12}}\)
D. \(\frac{{29}}{{30}}\)
Hướng dẫn
Chọn đáp án là: B
Phương pháp giải:
Tách \(5 = 1 + 1 + 1 + 1 + 1\) rồi thực hiện ghép 1 với \(\frac{{ – 1}}{2};\,\,\frac{{ – 5}}{6};\,\,\frac{{ – 11}}{{12}};\,\,\frac{{ – 19}}{{20}};\,\,\frac{{ – 29}}{{30}}\).
Ta có :
\(\begin{array}{l}5 – \frac{1}{2} – \frac{5}{6} – \frac{{11}}{{12}} – \frac{{19}}{{20}} – \frac{{29}}{{30}}\\ = \left( {1 – \frac{1}{2}} \right) + \left( {1 – \frac{5}{6}} \right) + \left( {1 – \frac{{11}}{{12}}} \right) + \left( {1 – \frac{{19}}{{20}}} \right) + \left( {1 – \frac{{29}}{{30}}} \right)\\ = \frac{1}{2} + \frac{1}{6} + \frac{1}{{12}} + \frac{1}{{20}} + \frac{1}{{30}}\\ = \frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + \frac{1}{{4.5}} + \frac{1}{{5.6}}\\ = 1 – \frac{1}{2} + \frac{1}{2} – \frac{1}{3} + \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + \frac{1}{5} – \frac{1}{6}\\ = 1 – \frac{1}{6}\\ = \frac{5}{6}\end{array}\)
Vậy kết quả của phép tính là: \(\frac{5}{6}\)
Chọn B
