$\text{So sánh:A}=\dfrac{2^{2021}-3}{2^{2020}-1}\text{vàB}=\dfrac{2^{2020}-3}{2^{2019}-1}$ 27/10/2021 Bởi Arianna $\text{So sánh:A}=\dfrac{2^{2021}-3}{2^{2020}-1}\text{vàB}=\dfrac{2^{2020}-3}{2^{2019}-1}$
$A=$$\dfrac{2^{2021}-3}{2^{2020} -1}$ =$\dfrac{(2^{2021}-2)-1}{2^{2020} -1}$=$2-$$\dfrac{1}{2^{2020} -1}$ $B=$$\dfrac{2^{2020}-3}{2^{2019} -1}$ =$\dfrac{(2^{2020}-2)-1}{2^{2019} -1}$=$2-$$\dfrac{1}{2^{2019} -1}$ Có $2^{2020}$ $-1>$$2^{2019}$$-1 >0$ ⇒$\dfrac{1}{2^{2020} -1}$ $<$$\dfrac{1}{2^{2019} -1}$ ⇒$2-$$\dfrac{1}{2^{2020} -1}$ $>$$2-$$\dfrac{1}{2^{2019} -1}$ ⇒$A>B$ Bình luận
Đáp án:
Bạn xem hình ảnh. Chúc bạn học tốt nhé!
Giải thích các bước giải:
$A=$$\dfrac{2^{2021}-3}{2^{2020} -1}$ =$\dfrac{(2^{2021}-2)-1}{2^{2020} -1}$=$2-$$\dfrac{1}{2^{2020} -1}$
$B=$$\dfrac{2^{2020}-3}{2^{2019} -1}$ =$\dfrac{(2^{2020}-2)-1}{2^{2019} -1}$=$2-$$\dfrac{1}{2^{2019} -1}$
Có $2^{2020}$ $-1>$$2^{2019}$$-1 >0$
⇒$\dfrac{1}{2^{2020} -1}$ $<$$\dfrac{1}{2^{2019} -1}$
⇒$2-$$\dfrac{1}{2^{2020} -1}$ $>$$2-$$\dfrac{1}{2^{2019} -1}$
⇒$A>B$