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a,\(A=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+...+\frac{1}{5^{100}}\)
\(=>5A=1+\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{99}}\)
\(=>5A-A=1-\frac{1}{5^{100}}=>A=\frac{1-\frac{1}{5^{100}}}{4}\)
b, Ta có \(1-\frac{1}{5^{100}}< 1=>\frac{1-\frac{1}{5^{100}}}{4}< \frac{1}{4}\)hay \(A< \frac{1}{4}\)
\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}>72^{43}\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
\(9^{100}và3^{200}=3^{200}và3^{200}\\ \Rightarrow3^{200}=3^{200}\\ \Rightarrow9^{100}=3^{200}.\\ 5^{23}và125^3=5^{23}và5^9\\ \Rightarrow5^{23}>5^9\\ \Rightarrow5^{23}>5^3.\)
9¹⁰⁰ = (3²)¹⁰⁰ = 3²⁰⁰
Vậy 9¹⁰⁰ = 3²⁰⁰
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125³ = (5³)³ = 5⁹
Do 23 > 9 nên 5²³ > 5⁹
Vậy 5²³ > 125³
\(B=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right)...\left(\frac{1}{100}-1\right)\)
\(B=\frac{-3}{4}.\frac{-8}{9}...\frac{-99}{100}\)
\(B=-\left(\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\right)\)
\(B=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{9.11}{10.10}\right)\)
\(B=-\left(\frac{1.2...9}{2.3...10}.\frac{3.4...11}{2.3...10}\right)\)
\(B=-\left(\frac{1}{10}.\frac{11}{2}\right)\)
\(B=\frac{-11}{20}< \frac{-11}{21}\)
Vậy \(B< \frac{-11}{21}\)
https://hoc24.vn/cau-hoi/help-me-so-sanh-437-va-38-510825.488777179563
Ta có :
4^37=(2^2)^37=2^74
3^8+5^10+8^25>8^25= (2^3)^25=2^25
Vì 2^74<2^75
=> 4^37 < 3^8 + 5^10+8^25
Vậy 4^37 < 3^8 + 5^10+8^25
Bài 8 : ( x ở đâu ??? )
Bài 9
2S = 2+ 22+23+24+...+210
2S - S =( 2+ 22+23+24+...+210) - ( 1+2+22+23+...+29)= 210 -1
S = 28.22-1 = 28.4-1
Vậy S < 5,28
Bài 10
7248= 7247.721 ; 7247=7247.1
7247=7246.721 ; 7246=7246.1
7248-7247= 7247.721-7247.1=7247.(72-1)
7247-7246=7246.721-7246.1= 7246.(72-1)
Vậy 7248-7247<7247-7246
~HT~
Lộn
7248 - 7247 > 7247 - 7246