so sánh 10 mũ 5/10 mũ 5 + 1 và 10 mũ 5 + 1/10 mũ 5 + 2 25/08/2021 Bởi Amaya so sánh 10 mũ 5/10 mũ 5 + 1 và 10 mũ 5 + 1/10 mũ 5 + 2
Ta có: $1-\frac{10^{5}}{10^{5}+1} = \frac{1}{10^{5}+1}$ $1-\frac{10^{5}+1}{10^{5}+2} = \frac{1}{10^{5}+2}$ Vì $10^{5}+1<10^{5}+2$ $⇒ \frac{1}{10^{5}+1}>\frac{1}{10^{5}+2}$ $⇒ -\frac{1}{10^{5}+1}<-\frac{1}{10^{5}+2}$ $⇒ 1-\frac{10^{5}}{10^{5}+1}<1-\frac{10^{5}+1}{10^{5}+2}$ $⇒ \frac{10^{5}}{10^{5}+1} <\frac{10^{5}+1}{10^{5}+2} $ Bình luận
Ta có $ \dfrac{10^5}{10^5 +1} = \dfrac{10^5 . (10^5+2)}{(10^5+1). (10^5 +2)} = \dfrac{10^{10} +2 . 10^5}{(10^5+1). (10^+2)} $ $ \dfrac{10^5 +1}{10^5+2} = \dfrac{ (10^5+1)(10^5+1)}{(10^5+1). (10^+2)} = \dfrac{10^5.(10^5+1) + 1.(10^5+1)}{(10^5+1). (10^+2)}$ $ = \dfrac{10^{10} + 10^5 + 10^5 + 1}{(10^5+1). (10^+2)} = \dfrac{10^{10} + 2. 10^5 +1}{(10^5+1). (10^+2)}$ Vì $ 10^{10} +2 . 10^5 < 10^{10} +2 . 10^5+1$ $\to \dfrac{10^{10} +2 . 10^5}{(10^5+1). (10^+2)} < \dfrac{10^{10} + 2. 10^5 +1}{(10^5+1). (10^+2)}$ $\to \dfrac{10^5}{10^5 +1} < \dfrac{10^5 +1}{10^5+2}$ Bình luận
Ta có: $1-\frac{10^{5}}{10^{5}+1} = \frac{1}{10^{5}+1}$
$1-\frac{10^{5}+1}{10^{5}+2} = \frac{1}{10^{5}+2}$
Vì $10^{5}+1<10^{5}+2$
$⇒ \frac{1}{10^{5}+1}>\frac{1}{10^{5}+2}$
$⇒ -\frac{1}{10^{5}+1}<-\frac{1}{10^{5}+2}$
$⇒ 1-\frac{10^{5}}{10^{5}+1}<1-\frac{10^{5}+1}{10^{5}+2}$
$⇒ \frac{10^{5}}{10^{5}+1} <\frac{10^{5}+1}{10^{5}+2} $
Ta có
$ \dfrac{10^5}{10^5 +1} = \dfrac{10^5 . (10^5+2)}{(10^5+1). (10^5 +2)} = \dfrac{10^{10} +2 . 10^5}{(10^5+1). (10^+2)} $
$ \dfrac{10^5 +1}{10^5+2} = \dfrac{ (10^5+1)(10^5+1)}{(10^5+1). (10^+2)} = \dfrac{10^5.(10^5+1) + 1.(10^5+1)}{(10^5+1). (10^+2)}$
$ = \dfrac{10^{10} + 10^5 + 10^5 + 1}{(10^5+1). (10^+2)} = \dfrac{10^{10} + 2. 10^5 +1}{(10^5+1). (10^+2)}$
Vì $ 10^{10} +2 . 10^5 < 10^{10} +2 . 10^5+1$
$\to \dfrac{10^{10} +2 . 10^5}{(10^5+1). (10^+2)} < \dfrac{10^{10} + 2. 10^5 +1}{(10^5+1). (10^+2)}$
$\to \dfrac{10^5}{10^5 +1} < \dfrac{10^5 +1}{10^5+2}$