So sánh:
A=\(\dfrac{7^{2011}+1}{7^{2013}+1}\) và B=\(\dfrac{7^{2013}+1}{7^{2015}+1}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
HJ
0
9 tháng 7 2017
b, Ta có:
\(14A=\dfrac{7^{2013}+14}{7^{2013}+1}=\dfrac{7^{2013}+1+13}{7^{2013}+1}=\dfrac{7^{2013}+1}{7^{2013}+1}+\dfrac{13}{7^{2013}+1}=1+\dfrac{13}{7^{2013}+1}\)
\(14B=\dfrac{7^{2015}+14}{7^{2015}+1}=\dfrac{7^{2015}+1+13}{7^{2015}+1}=\dfrac{7^{2015}+1}{7^{2015}+1}+\dfrac{13}{7^{2015}+1}=1+\dfrac{13}{7^{2015}+1}\)
\(\)Vì \(7^{2013}+1< 7^{2015}+1\)
\(\dfrac{\Rightarrow13}{7^{2013}+1}>\dfrac{13}{7^{2015}+1}\)
\(\Rightarrow1+\dfrac{13}{7^{2013}+1}>1+\dfrac{13}{7^{2015+1}}\)
\(\Leftrightarrow14A>14B\)
\(\Rightarrow A>B\)
28 tháng 2 2021
Bạn thiếu đề rồi phải là trừ hay cộng j j chứ.
Xét:
`A+B=2+1/2+1/3+1/4+......+1/4026+1/3+1/5+1/7+......+1/4025`
`1/2+1/3+1/4+......+1/4026+1/3+1/5+1/7+......+1/4025>0`
`=>A+B>2`
Mà `1 2013/2014<2`
`=>A+B>1 2013/2014`
2N
3
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
14 tháng 11 2019
\(\frac{A}{B}=\frac{7^{2013}+1}{7^{2014}+1}.\frac{7^{2015}+1}{7^{2014}+1}=\frac{7^{4028}+7^{2013}+7^{2015}+1}{7^{4028}+2.7^{2014}+1}=\)
\(=\frac{7^{4028}+7^{2013}\left(1+7^2\right)+1}{7^{4028}+2.7.7^{2013}+1}=\frac{7^{4028}+50.7^{2013}+1}{7^{4028}+14.7^{2013}+1}>1\)
\(\Rightarrow A>B\)
NH
0
Xét hiệu:
\(C=1-\dfrac{7^{2011}+1}{7^{2013}+1}=\dfrac{7^{2011}\left(7^2-1\right)}{7^{2013}+1}=\dfrac{48.7^{2011}}{7^{2013}+1}\)
\(D=1-\dfrac{7^{2013}+1}{7^{2015}+1}=\dfrac{7^{2013}\left(7^2-1\right)}{7^{2015}+1}=\dfrac{48.7^{2013}}{7^{2015}+1}\)
Ta có:
\(\dfrac{C}{D}=\dfrac{48.7^{2011}}{7^{2013}+1}\cdot\dfrac{7^{2015}+1}{48.7^{2013}}=\dfrac{7^{2015}+1}{\left(7^{2013}+1\right)\cdot7^2}=\dfrac{7^{2015}+1}{7^{2015}+49}< 1\)
=> C<D =>A>B