Toán Cho B = 1/4 +1/5+1/6+…+1/19 . Hãy chứng tỏ B>1 22/07/2021 By Katherine Cho B = 1/4 +1/5+1/6+…+1/19 . Hãy chứng tỏ B>1
`B = 1/4 + 1/5 + 1/6 + … + 1/19` `B = 1/4 + (1/5 + 1/6 + 1/7 + … + 1/9) + (1/10 + 1/11 + 1/12 + … + 1/19)` Ta có: `1/9 . 5 = 5/9` `1/19 . 10 = 10/19` Vì: `1/5 + 1/6 + 1/7 + … + 1/9 > 5/9` `1/10 + 1/11 + 1/12 + … + 1/19 > 10/19 > 1/2` `=> B > 5/9 + 1/2 + 1/4 > 1` `=> B > 1` Vậy `B > 1` Trả lời
B =$\frac{1}{4}$ + $\frac{1}{5}$ + $\frac{1}{6}$ +…+ $\frac{1}{19}$ = $\frac{1}{4}$ + ($\frac{1}{5}$ + $\frac{1}{6}$ +…+$\frac{1}{9}$) + ($\frac{1}{10}$ + $\frac{1}{11}$ +..+ $\frac{1}{19}$) Có : $\frac{1}{5}$ + $\frac{1}{6}$ +…+$\frac{1}{9}$ < $\frac{1}{9}$ + $\frac{1}{9}$ +…+$\frac{1}{9}$ = $\frac{1}{9}$ . 5 = $\frac{5}{9}$ > $\frac{1}{2}$ $\frac{1}{10}$ + $\frac{1}{11}$ +..+ $\frac{1}{19}$ < $\frac{1}{19}$ + $\frac{1}{19}$ +..+ $\frac{1}{19}$) = $\frac{1}{19}$ . 10 = $\frac{10}{19}$ > $\frac{1}{2}$ Vì B > $\frac{1}{4}$ + $\frac{1}{2}$ + $\frac{1}{2}$ > 1 Nên B > 1 Trả lời
`B = 1/4 + 1/5 + 1/6 + … + 1/19`
`B = 1/4 + (1/5 + 1/6 + 1/7 + … + 1/9) + (1/10 + 1/11 + 1/12 + … + 1/19)`
Ta có:
`1/9 . 5 = 5/9`
`1/19 . 10 = 10/19`
Vì:
`1/5 + 1/6 + 1/7 + … + 1/9 > 5/9`
`1/10 + 1/11 + 1/12 + … + 1/19 > 10/19 > 1/2`
`=> B > 5/9 + 1/2 + 1/4 > 1`
`=> B > 1`
Vậy `B > 1`
B =$\frac{1}{4}$ + $\frac{1}{5}$ + $\frac{1}{6}$ +…+ $\frac{1}{19}$
= $\frac{1}{4}$ + ($\frac{1}{5}$ + $\frac{1}{6}$ +…+$\frac{1}{9}$) + ($\frac{1}{10}$ + $\frac{1}{11}$ +..+ $\frac{1}{19}$)
Có : $\frac{1}{5}$ + $\frac{1}{6}$ +…+$\frac{1}{9}$ < $\frac{1}{9}$ + $\frac{1}{9}$ +…+$\frac{1}{9}$
= $\frac{1}{9}$ . 5 = $\frac{5}{9}$ > $\frac{1}{2}$
$\frac{1}{10}$ + $\frac{1}{11}$ +..+ $\frac{1}{19}$ < $\frac{1}{19}$ + $\frac{1}{19}$ +..+ $\frac{1}{19}$)
= $\frac{1}{19}$ . 10 = $\frac{10}{19}$ > $\frac{1}{2}$
Vì B > $\frac{1}{4}$ + $\frac{1}{2}$ + $\frac{1}{2}$ > 1
Nên B > 1