A=\(\dfrac{13^{15}+1}{13^{16}+1}\) và B= \(\dfrac{13^{16}+1}{13^{17}+1}\)
so sánh A và B
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TM
0
DT
2
29 tháng 10 2016
Ta có:
\(A=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13A=\frac{13^{16}+13}{13^{16}+1}=\frac{13^{16}+1+12}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)
\(B=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13B=\frac{13^{17}+13}{13^{17}+1}=\frac{13^{17}+1+12}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)
Ta thấy:
\(13^{16}+1< 13^{17}+1\)
\(\Rightarrow\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)
\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)
hay \(A>B\)
Vậy \(A>B.\)
DT
2
1 tháng 8 2017
a) \(\dfrac{12}{47}\) và \(\dfrac{11}{53}\)
Ta có: \(\dfrac{11}{47}>\dfrac{11}{53}\) mà \(\dfrac{12}{47}>\dfrac{11}{47}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)
1 tháng 8 2017
a) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{11}{44}>\dfrac{11}{53}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)
b) Ta có : \(\dfrac{456}{461}=1-\dfrac{5}{461}\)
\(\dfrac{123}{128}=1-\dfrac{5}{128}\)
Vì \(\dfrac{5}{461}< \dfrac{5}{128}\Rightarrow1-\dfrac{5}{461}>1-\dfrac{5}{128}\)
\(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\)
c) Ta có :\(\dfrac{12}{47}>\dfrac{12}{48}=\dfrac{1}{4}=\dfrac{19}{76}>\dfrac{19}{77}\)
=> \(\dfrac{12}{47}>\dfrac{19}{77}\)
d) Ta có : \(13A=13.\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{16}+13}{13^{16}+1}=\dfrac{13^{16}+1+12}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(13B=13.\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
Ta thấy : \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\Rightarrow\dfrac{13^{15}+1}{13^{16}+1}>\dfrac{13^{16}+1}{13^{17}+1}\)
ND
Nguyễn Đức Trí
VIP
12 tháng 9 2023
a) \(\dfrac{17}{20}< \dfrac{18}{20}< \dfrac{18}{19}\Rightarrow\dfrac{17}{20}< \dfrac{18}{19}\)
b) \(\dfrac{19}{18}>\dfrac{19+2024}{18+2024}=\dfrac{2023}{2022}\Rightarrow\dfrac{19}{18}>\dfrac{2023}{2022}\)
c) \(\dfrac{135}{175}=\dfrac{27}{35}\)
\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)
\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)
DH
1
23 tháng 6 2022
\(A=\dfrac{13^{15}+1}{13^{16}+1}\)
\(\Leftrightarrow13A=\dfrac{13^{16}+13}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(B=\dfrac{13^{16}+1}{13^{17}+1}\)
\(\Leftrightarrow13B=\dfrac{13^{17}+13}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
mà \(13^{16}+1< 13^{17}+1\)
nên A>B
14 tháng 3 2020
Bài 1:
Ta có:
\(\left(\frac{1}{10}\right)^{15}=\left(\frac{1}{5}\right)^{3.5}=\left(\frac{1}{125}\right)^5\)
\(\left(\frac{3}{10}\right)^{20}=\left(\frac{3}{10}\right)^{4.5}=\left(\frac{81}{10000}\right)^5\)
Lại có:
\(\frac{1}{125}=\frac{80}{10000}< \frac{81}{10000}\Rightarrow\left(\frac{1}{125}\right)^5< \left(\frac{81}{10000}\right)^5\)
\(\Rightarrow\left(\frac{1}{10}\right)^{15}< \left(\frac{3}{10}\right)^{20}\)
14 tháng 3 2020
Bài 2:
Ta có:
\(A=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13A=\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)
\(B=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13B=\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)
Mà \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)
\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)
\(\Rightarrow13A>13B\Rightarrow A>B\)
\(ta có A=\dfrac{13^{15}+1}{13^{16}+1}=\dfrac{13^{15}}{13^{16}}+1\)=\(\dfrac{1}{13}+1\)
B=\(\dfrac{13^{16}+1}{13^{17}+1}=\dfrac{13^{16}}{13^{17}}+1\)=\(\dfrac{1}{13}+1\)
vậy A=B
hơi sai sai r
a=\(\dfrac{(13)^{15}+1}{(13)^{16}+1} =\dfrac{(13)^{15}+1}{13.(13)^{15}+1}=\dfrac{1}{3}\)
b=\(\dfrac{(13)^{16}+1}{(13)^{17}+1} =\dfrac{(13)^{16}+1}{13.(13)^{16}+1}=\dfrac{1}{13}\)
=> a=b