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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SO SÁNH A VÀ B
A= 13^16 + 1/13^17+1 VÀ B=13^15 +1 /13^16+1
A=1999^2000 +1 / 1999^1999 +1 VÀ B=1999^1999+1/1999^1998 +1
so sánh A và B biết A= 1315 +1/ 1316+1; B=1316+1/ 1317+1
A=\(\frac{13^{15}+1}{13^{16}+1}\)
B=\(\frac{13^{16}+1}{13^{17}+1}\)
Hãy so sánh A và B
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 \(A>B.\)
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Ta có: \(\frac{a}{b}< \frac{a+c}{b+c}\)
=> \(B=\frac{13^{16}+1}{13^{17}+1}< \frac{13^{16}+1+12}{13^{17}+1+12}=\frac{13^{16}+13}{13^{17}+13}=\frac{13\left(13^{15}+1\right)}{13\left(13^{16}+1\right)}=\frac{13^{15}+1}{13^{16}+1}=A\)
Vậy: \(A>B\)
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A=\(\frac{13^{15}+1}{13^{16}+1}\)và B=\(\frac{13^{16}+1}{13^{17}+1}\)Hãy so sánh A và B.
Ta có: \(13A=1+\frac{12}{13^{16}+1};13B=1+\frac{12}{13^{17}+1}\)
Do \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\). Nên \(13A>13B\)
Vậy \(A>B\)
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So sánh
a, A = \(\frac{13^{15}+1}{13^{16}+1}\) và B = \(\frac{13^{16}+1}{13^{17}+1}\)
1 tháng 8 2017 lúc 20:03
Mina giúp mk vs!!!!!!!!!!
1)So sánh
a)dfrac{12}{47}vàdfrac{11}{53} b)dfrac{456}{461}vàdfrac{123}{128} c)dfrac{12}{47}vàdfrac{19}{77}
d)Adfrac{13^{15}+1}{13^{16}+1}và Bdfrac{13^{16}+1}{13^{17}+1}
P/s:Cherry Võ tag Trần Huyền Trang giùm cái please
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Mina giúp mk vs!!!!!!!!!!
1)So sánh
a)\(\dfrac{12}{47}và\dfrac{11}{53}\) b)\(\dfrac{456}{461}và\dfrac{123}{128}\) c)\(\dfrac{12}{47}và\dfrac{19}{77}\)
d)\(A=\dfrac{13^{15}+1}{13^{16}+1}và\) \(B=\dfrac{13^{16}+1}{13^{17}+1}\)
P/s:Cherry Võ tag Trần Huyền Trang giùm cái please
a) \(\dfrac{12}{47}\) và \(\dfrac{11}{53}\)
Ta có: \(\dfrac{11}{47}>\dfrac{11}{53}\) mà \(\dfrac{12}{47}>\dfrac{11}{47}\)
\(\Rightarrow\dfrac{12}{47}>\dfrac{11}{53}\)
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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 : \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\Rightarrow\dfrac{13^{15}+1}{13^{16}+1}>\dfrac{13^{16}+1}{13^{17}+1}\)
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a) Ta có : \(\dfrac{12}{47}>\dfrac{12}{53}>\dfrac{11}{53}\) \(\Leftrightarrow\dfrac{12}{47}>\dfrac{11}{53}\) b) Ta có : \(\dfrac{456}{461}=\dfrac{461-5}{461}=1-\dfrac{5}{461}\) \(\dfrac{123}{128}=\dfrac{128-5}{128}=1-\dfrac{5}{128}\) Do \(1-\dfrac{5}{461}>1-\dfrac{5}{128}\) \(\Rightarrow\dfrac{456}{461}>\dfrac{123}{128}\) c) Ta có: \(\dfrac{12}{47}\) > \(\dfrac{12}{48}=\dfrac{1}{4}\) \(\dfrac{19}{77}< \dfrac{19}{76}=\dfrac{1}{4}\) Do \(\dfrac{12}{47}>\dfrac{1}{4}>\dfrac{19}{77}\) \(\Rightarrow\dfrac{12}{47}>\dfrac{19}{77}\) d) Ta có : A=\(\dfrac{13^{15}+1}{13^{16}+1}\) \(\Leftrightarrow\) 13A=\(\dfrac{13.\left(13^{15}+1\right)}{13^{16}+1}\) \(\Leftrightarrow\) 13A=\(\dfrac{13^{16}+13}{13^{16}+1}\) \(=\dfrac{13^{16}+1+12}{13^{16}+1}=\dfrac{13^{16}+1}{13^{16}+1}+\dfrac{12}{13^{16}+1}\)
\(=1+\dfrac{12}{13^{16}+1}\) B=\(\dfrac{13^{16}+1}{13^{17}+1}\) \(\Leftrightarrow\) 13B=\(\dfrac{13.\left(13^{16}+1\right)}{13^{17}+1}\)
\(\Leftrightarrow\) 13B=\(\dfrac{13^{17}+13}{13^{17}+1}=\dfrac{13^{17}+1+12}{13^{17}+1}\) \(=\dfrac{13^{17}+1}{13^{17}+1}+\dfrac{12}{13^{17}+1}\) \(=1+\dfrac{12}{13^{17}+1}\)
Do \(1+\dfrac{12}{13^{16}+1}.>1+\dfrac{12}{13^{17}+1}\) nên 13A>13B \(\Rightarrow\) A>B
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Xem thêm câu trả lời
So sánh
a)17/20 và 18/19 b)19/18 và 2023/2022
c)13/17 và 135/175 d)53/63 và 535/636
e)13/15 và 22/25 \(\dfrac{2023}{2023^2+1}và\dfrac{2022}{2022^2+1}\)
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) \(\dfrac{135}{175}=\dfrac{27}{35}\)
\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)
\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)
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1)so sánh
\(\dfrac{15^{15}+1}{13^{16}+1}\)và\(\dfrac{13^{16}+1}{13^{17}+1}\)
\(A=\dfrac{13^{15}+1}{13^{16}+1}\)
\(\Leftrightarrow13A=\dfrac{13^{16}+13}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(B=\dfrac{13^{16}+1}{13^{17}+1}\)
\(\Leftrightarrow13B=\dfrac{13^{17}+13}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
mà \(13^{16}+1< 13^{17}+1\)
nên A>B
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Bài 1 : So sánh
\(\left(\frac{1}{10}\right)^{15}\) và \(\left(\frac{3}{10}\right)^{20}\)
Bài 2 : So sánh
A = \(\left(\frac{13^{15}+1}{13^{16}+1}\right)\) và B = \(\left(\frac{13^{16}+1}{13^{17}+1}\right)\)
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:
\(\frac{1}{125}=\frac{80}{10000}< \frac{81}{10000}\Rightarrow\left(\frac{1}{125}\right)^5< \left(\frac{81}{10000}\right)^5\)
\(\Rightarrow\left(\frac{1}{10}\right)^{15}< \left(\frac{3}{10}\right)^{20}\)
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 \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)
\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)
\(\Rightarrow13A>13B\Rightarrow A>B\)