A=\(\dfrac{100^{10+1}}{100^{10-1}}\)và B=\(\dfrac{100^{10-1}}{100^{10-3}}\)
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DA
4
9 tháng 2 2023
ta có:
1/10.A=10100+1/10(1099+1)
1/10.A=10100+1/10100+10
1/10.A=1-(9/10100+10)
1/10.B=10101+1/10(10100+1)
1/10.B=10101+1/10101+10
1/10.B=1-(9/10101+10)
vì(10101+10)>(10100+1)=> 9/10101+10 < 9/10100+10 => 1-(9/10101+10) > 1-(9/10100+10)
hay 1/10.A>1/10.B
=>A>B
9 tháng 2 2023
ta có:
1/10.A=10100+1/10(1099+1)
1/10.A=10100+1/10100+10
1/10.A=1-(9/10100+10)
1/10.B=10101+1/10(10100+1)
1/10.B=10101+1/10101+10
1/10.B=1-(9/10101+10)
vì(10101+10)>(10100+1)=> 9/10101+10 < 9/10100+10 => 1-(9/10101+10) < 1-(9/10100+10)
hay 1/10.A<1/10.B
=>A<B
H9
HT.Phong (9A5)
CTVHS
17 tháng 10 2023
a) \(\dfrac{1}{10}=0,1\)
\(\dfrac{1}{100}=0,01\)
\(\dfrac{1}{1000}=0,001\)
\(\dfrac{1}{10000}=0,0001\)
b) \(\dfrac{84}{10}=8,4\)
\(\dfrac{225}{100}=2,25\)
\(\dfrac{6453}{100}=64,53\)
\(\dfrac{25789}{10000}=2,5789\)
AD
3
PN
12 tháng 8 2017
\(A=\dfrac{10^{99}+1}{10^{100}+1}\)
\(\Leftrightarrow10A=\dfrac{10\left(10^{99}+1\right)}{10^{100}+1}\)
\(\Leftrightarrow10A=\dfrac{10^{100}+10}{10^{100}+1}=\dfrac{10^{100}+1+9}{10^{100}+1}=1+\dfrac{9}{10^{100}+1}\)
\(B=\dfrac{10^{100}+1}{10^{101}+1}\)
\(\Leftrightarrow10B=\dfrac{10\left(10^{100}+1\right)}{10^{101}+1}\)
\(\Leftrightarrow10B=\dfrac{10^{101}+10}{10^{101}+1}=\dfrac{10^{101}+1+9}{10^{101}+1}=1+\dfrac{9}{10^{101}+1}\)
Do \(\dfrac{9}{10^{100}+1}>\dfrac{9}{10^{101}+1}\) nên \(10A>10B\)
\(\Rightarrow A>B\)
12 tháng 8 2017
Áp dụng tính chất:
\(\dfrac{a}{b}< 1\Rightarrow\dfrac{a+m}{b+m}< 1\left(m\in N\right)\)
\(B=\dfrac{10^{100}+1}{10^{101}+1}< 1\)
\(B< \dfrac{10^{100}+1+9}{10^{101}+1+9}\)
\(B< \dfrac{10^{100}+10}{10^{101}+10}\)
\(B< \dfrac{10\left(10^{99}+1\right)}{10\left(10^{100}+1\right)}\)
\(B< \dfrac{10^{99}+1}{10^{100}+1}=A\)
\(B< A\)
NA
Ngoc Anh Thai
Giáo viên
12 tháng 4 2021
\(A=\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}...\dfrac{99}{100}\\ < \dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{97}{98}.\dfrac{98}{99}< \dfrac{1}{99}\\ < \dfrac{1}{10}.\\\\ =>A< \dfrac{1}{10}\)
Ta có :
\(A=\dfrac{100^{10}+1}{100^{10}-1}=\dfrac{100^{10}-1+2}{100^{10}-1}=\dfrac{100^{10}-1}{100^{10}-1}+\dfrac{2}{100^{10}-1}=1+\dfrac{2}{100^{10}-1}\)
\(B=\dfrac{100^{10}-1}{100^{10}-3}=\dfrac{100^{10}-3+2}{100^{10}-3}=\dfrac{100^{10}-3}{100^{10}-3}+\dfrac{2}{100^{10}-3}=1+\dfrac{2}{100^{10}-3}\)
\(\) Vì \(1+\dfrac{2}{100^{10}-1}< 1+\dfrac{2}{100^{10}-3}\Rightarrow A< B\)
good