Tính nhanh: 1/ 20 + 1/ 30 +..

11/11

Tính nhanh:

\[\frac{1}{{20}}\] + \[\frac{1}{{30}}\] + \[\frac{1}{{42}}\]+ \[\frac{1}{{56}}\] + \[\frac{1}{{72}}\] + \[\frac{1}{{90}}\] + \[\frac{1}{{110}}\] + \[\frac{1}{{132}}\]

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Giải thích

Tính nhanh:

\[\frac{1}{{20}}\] + \[\frac{1}{{30}}\] + \[\frac{1}{{42}}\]+ \[\frac{1}{{56}}\] + \[\frac{1}{{72}}\] + \[\frac{1}{{90}}\] + \[\frac{1}{{110}}\] + \[\frac{1}{{132}}\]

= \[\frac{1}{{4 \times 5}}\] + \[\frac{1}{{5 \times 6}}\] + \[\frac{1}{{6 \times 7}}\] + \[\frac{1}{{7 \times 8}}\] + \[\frac{1}{{8 \times 9}}\] + \[\frac{1}{{9 \times 10}}\] + \[\frac{1}{{10 \times 11}}\] +\[\frac{1}{{11 \times 12}}\]

= \[\frac{1}{4}\] – \[\frac{1}{5}\] + \[\frac{1}{5}\] – \[\frac{1}{6}\] + \[\frac{1}{6}\] – \[\frac{1}{7}\] + \[\frac{1}{7}\] – \[\frac{1}{8}\] + \[\frac{1}{8}\] – \[\frac{1}{9}\] + \[\frac{1}{9}\] – \[\frac{1}{{10}}\] + \[\frac{1}{{10}}\] – \[\frac{1}{{11}}\] + \[\frac{1}{{11}}\] – \[\frac{1}{{12}}\]

= \[\frac{1}{4}\] – \[\frac{1}{{12}}\]

= \[\frac{1}{6}\]