So sánh A và B biết A= (15^2015+1)/(15^2016+1) và B=(15^2014+1)/(15^2015+1) 29/09/2021 Bởi Kennedy So sánh A và B biết A= (15^2015+1)/(15^2016+1) và B=(15^2014+1)/(15^2015+1)
Đáp án+Giải thích các bước giải: $A=\dfrac{15^{2015}+1}{15^{2016}+1}\\=>15A=\dfrac{15^{2016}+15}{15^{2016}+1}\\15A=\dfrac{15^{2016}+1+14}{15^{2016}+1}\\=\dfrac{15^{2016}+1}{15^{2016}+1}+\dfrac{14}{15^{2016}+1}\\=1+\dfrac{14}{15^{2016}+1}$ $B=\dfrac{15^{2014}+1}{15^{2015}+1}\\=>15B=\dfrac{15^{2015}+15}{15^{2015}+1}\\15B=\dfrac{15^{2015}+1+14}{15^{2015}+1}\\=\dfrac{15^{2015}+1}{15^{2015}+1}+\dfrac{14}{15^{2015}+1}\\=1+\dfrac{14}{15^{2015}+1}$ $\text{Vì $15^{2016}+1 >10^{2015}+1$}\\=>\dfrac{14}{15^{2016}+1}<\dfrac{14}{15^{2015}+1}\\=>15A<15B\\=>A<B$ Bình luận
Xin hay nhất cho nhóm ạ ^_^
Đáp án+Giải thích các bước giải:
$A=\dfrac{15^{2015}+1}{15^{2016}+1}\\=>15A=\dfrac{15^{2016}+15}{15^{2016}+1}\\15A=\dfrac{15^{2016}+1+14}{15^{2016}+1}\\=\dfrac{15^{2016}+1}{15^{2016}+1}+\dfrac{14}{15^{2016}+1}\\=1+\dfrac{14}{15^{2016}+1}$ $B=\dfrac{15^{2014}+1}{15^{2015}+1}\\=>15B=\dfrac{15^{2015}+15}{15^{2015}+1}\\15B=\dfrac{15^{2015}+1+14}{15^{2015}+1}\\=\dfrac{15^{2015}+1}{15^{2015}+1}+\dfrac{14}{15^{2015}+1}\\=1+\dfrac{14}{15^{2015}+1}$ $\text{Vì $15^{2016}+1 >10^{2015}+1$}\\=>\dfrac{14}{15^{2016}+1}<\dfrac{14}{15^{2015}+1}\\=>15A<15B\\=>A<B$