Chứng minh rằng : 1/12+1/13+1/14+…..+1/22>1/2 mọi người giúp mình nha 29/11/2021 Bởi Liliana Chứng minh rằng : 1/12+1/13+1/14+…..+1/22>1/2 mọi người giúp mình nha
Đáp án: Giải thích các bước giải: $\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}$ $ $ Ta có: $\dfrac{1}{12}>\dfrac{1}{22}$ ; $\dfrac{1}{13}>\dfrac{1}{22}$ ; … ; $\dfrac{1}{22}=\dfrac{1}{22}$ $ $ $⇒\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}>\dfrac{1}{22}+\dfrac{1}{22}+…+\dfrac{1}{22}$ $ $ $⇒\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}>\dfrac{1}{2}$ (đpcm) Bình luận
Ta có 1/12>1/22 1/13>1/22 1/14>1/22 …….. 1/22=1/22 =>1/12+1/13+1/14+…+1/22>1/22+1/22+1/22+..+1/22=1/2 Bình luận
Đáp án:
Giải thích các bước giải:
$\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}$
$ $
Ta có: $\dfrac{1}{12}>\dfrac{1}{22}$ ; $\dfrac{1}{13}>\dfrac{1}{22}$ ; … ; $\dfrac{1}{22}=\dfrac{1}{22}$
$ $
$⇒\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}>\dfrac{1}{22}+\dfrac{1}{22}+…+\dfrac{1}{22}$
$ $
$⇒\dfrac{1}{12}+\dfrac{1}{13}+\dfrac{1}{14}+…+\dfrac{1}{22}>\dfrac{1}{2}$ (đpcm)
Ta có
1/12>1/22
1/13>1/22
1/14>1/22
……..
1/22=1/22
=>1/12+1/13+1/14+…+1/22>1/22+1/22+1/22+..+1/22=1/2