Cho M = 1/10 + 1/15 + 1/21 + 1/28 + …. + 1/105 + 1/120 Chứng tỏ 1/3 < M < 1/2

17/08/2021 Bởi Claire

Cho M = 1/10 + 1/15 + 1/21 + 1/28 + …. + 1/105 + 1/120
Chứng tỏ 1/3 < M < 1/2

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giangnguyen

17/08/2021 vào lúc 01:56

M $= \frac{1}{10} + \frac{1}{15} + \frac{1}{21} + \frac{1}{28} + ... . + \frac{1}{105} + \frac{1}{120}$

M $= \frac{2}{20} + \frac{2}{30} + \frac{2}{42} + \frac{2}{56} + ... + \frac{2}{210} + \frac{2}{240}$

M $= \frac{2}{4.5} + \frac{2}{5.6} + \frac{2}{6.7} + \frac{2}{7.8} + ... + \frac{2}{14.15} + \frac{2}{15.16}$

$= \frac{2}{4.5} + \frac{2}{5.6} + \frac{2}{6.7} + \frac{2}{7.8} + ... + \frac{2}{14.15} + \frac{2}{15.16}$ M= $= \frac{2}{4} - \frac{2}{5} + \frac{2}{5} - \frac{2}{6} + \frac{2}{6} - \frac{2}{7} + \frac{2}{7} - \frac{2}{8} + ... + \frac{2}{15} - \frac{2}{16}$

M $= \frac{2}{4} - \frac{2}{16} = \frac{3}{8}$

$\frac{1}{3} <$ M $< \frac{1}{2}$ nên $\frac{1}{3} < \frac{3}{8} < \frac{1}{2}$

⇒ Chứng tỏ $\frac{1}{3} <$ M $< \frac{1}{2}$
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ngocdiep

17/08/2021 vào lúc 01:57

$#Mon lì$

Đáp án:

M `= 1/10 + 1/15 + 1/21 + 1/28 + …. + 1/105 + 1/120`

M`=2/20+2/30+2/42+2/56+…+2/210+2/240`

M`=2/ 4.5+2/ 5.6+2/ 6.7+2/ 7.8+…+2/ 14.15+2/ 15.16`

M`=2/4-2/5+2/5-2/6+2/6-2/7+2/7-2/8+…+2/15-2/16`

M`=2/4-2/16=3/8`

`1/3 <` M `< 1/2` nên `1/3 < 3/8 < 1/2`

⇒ Chứng tỏ `1/3 <` M `< 1/2`

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