s0 sanh
\(\frac{2^{23}+1}{2^{25}+1}\) vs \(\frac{2^{25}+1}{2^{27}+1}\)
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so sánh
a, \(\frac{2^{23^{ }}+1}{2^{25^{ }}+1}\)và \(\frac{2^{25^{ }}+1}{2^{27^{ }}+1}\)
b, 223+1 và 227+1
So sánh 2 phân số sau:
\(\frac{2^{23}+1}{2^{25}+1}va\frac{2^{25}+1}{2^{27}+1}\)
Vì \(2^{25}+1< 2^{27}+1\) nên \(\frac{2^{25}+1}{2^{27}+1}< 1\)
\(\Rightarrow\frac{2^{25}+1}{2^{27}+1}< \frac{2^{25}+1+3}{2^{27}+1+3}=\frac{2^{25}+4}{2^{27}+4}=\frac{2^2\left(2^{23}+1\right)}{2^2\left(2^{25}+1\right)}=\frac{2^{23}+1}{2^{25}+1}\)
Vậy \(\frac{2^{25}+1}{2^{27}+1}< \frac{2^{23}+1}{2^{25}+1}\)
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so sánh
x=\(\frac{2^{23}+1}{2^{25}+1}\)và y=\(\frac{2^{25}+1}{2^{27}+1}\)
X=2^23+1/2^25+1 = 1/2^2+1 = 1/4+1 = 1/5
Y=2^25+1/2^27+1 = 1/2^2+1 = 1/4+1 =1/ 5
Vì 1/5 = 1/5 nên X=Y
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Giúp tớ bài này nhé !
SO SÁNH:
\(\frac{2^{23}+1}{2^{25}+1}\)và\(\frac{2^{25}+1}{2^{27}+1}\)
Gọi 223+1/225+1 là A;225+1/227+1 là B
Ta có 22A=225+4/225+1
22A=225+1/225+1 + 3/225+1
22A=1+3/225+1
Có 22B=227+4/227+1
22B=227+1/227+1 + 3/227+1
22B=1+3/227+1
Vì 1+3/225+1>1+3/227+1
nên 22A>22B
nên A>B
Vậy A>B
Cảm ơn Pé's Pơ's nhiều nha
Ta có:\(\frac{a}{b}< \frac{a+c}{b+c}\)
\(\Leftrightarrow\frac{2^{25}+1}{2^{27}+1}< \frac{2^{25}+1+1}{2^{27}+1+1}=\frac{2^{25}+2}{2^{27}+2}=\frac{2^2.\left(2^{23}+1\right)}{2^2.\left(2^{25}+1\right)}=\frac{2^{23}+1}{2^{25}+1}\)
\(\Rightarrow\frac{2^{23}+1}{2^{25}+1}>\frac{2^{25}+1}{2^{27}+1}\)
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So sánh\(\frac{2^{23}+1}{2^{25}+1}\) và \(\frac{2^{25}+1}{2^{27}+1}\)
Ta có:
\(A=\frac{2^{23}+1}{2^{25}+1}\Rightarrow2A=\frac{2^{25}+2}{2^{25}+1}=1+\frac{1}{2^{25}+1}\)
\(B=\frac{2^{25}+1}{2^{27}+1}\Rightarrow2B=\frac{2^{27}+2}{2^{27}+1}=1+\frac{1}{2^{27}+1}\)
\(\frac{1}{2^{25}+1}>\frac{1}{2^{27}+1}\Rightarrow2A>2B\Rightarrow A>B\)
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So sánh: \(\frac{2^{23}+1}{2^{25}+1}\) và \(\frac{2^{25}+1}{2^{27}+1}\)
Bài 2 : Tínha) frac{10}{27}+frac{7}{23}+0,5-frac{5}{27}+frac{16}{23}B) frac{3}{8}.frac{27}{5}+frac{51}{5}frac{3}{8}+19C) 25.left(frac{-1}{5}right)^3+frac{1}{5}-2.left(frac{1}{2}right)^2-frac{1}{2}D) frac{35}{6}:left(frac{-4}{5}right)-frac{1}{129}:left(frac{4}{5}right)Mọi người giúp mình vs, mình tick cho
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Bài 2 : Tính
a) \(\frac{10}{27}+\frac{7}{23}+0,5-\frac{5}{27}+\frac{16}{23}\)
B) \(\frac{3}{8}.\frac{27}{5}+\frac{51}{5}\frac{3}{8}+19\)
C) \(25.\left(\frac{-1}{5}\right)^3+\frac{1}{5}-2.\left(\frac{1}{2}\right)^2-\frac{1}{2}\)
D) \(\frac{35}{6}:\left(\frac{-4}{5}\right)-\frac{1}{129}:\left(\frac{4}{5}\right)\)
Mọi người giúp mình vs, mình tick cho
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\(Chứngtỏrằng:\frac{1}{^22}+\frac{1}{^23}+\frac{1}{^24}+\frac{1}{^25}+\frac{1}{^26}+\frac{1}{^27}+\frac{1}{^28}< 1\)
chứng tỏ rằng 1 phần 2 mũ 2+1 phần ba mũ 2...........
giải luôn; đặt A=1/2^2+1/3^2+...+1/8^2
1/2^2 < 1/1.2
1/3^2<1/2.3
.......
1/8^2<1/7.8
=> 1/2^2 + 1/3^2 +...+1/8^2<1/1.2 + 1/2.3 + ....+ 1/7.8
=>A<1-1/2 + 1/2 - 1/3 + ....+1/7-1/8
=>A<1-1/8<1
vậy 1/2^2+1/3^2+....+1/8^2 <1
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a) frac{x-23}{24}+frac{x-23}{25}frac{x-23}{26}+frac{x-23}{27}Leftrightarrowfrac{x-23}{24}+frac{x-23}{25}-frac{x-23}{26}-frac{x-23}{27}0Leftrightarrowleft(x-23right)left(frac{1}{24}+frac{1}{25}-frac{1}{26}-frac{1}{27}right)0Leftrightarrow x-230( vì frac{1}{24}+frac{1}{25}-frac{1}{26}-frac{1}{27}ne0)Leftrightarrow x23Vậy nghiệm của pt x23
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a) \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\)
\(\Leftrightarrow\frac{x-23}{24}+\frac{x-23}{25}-\frac{x-23}{26}-\frac{x-23}{27}=0\)
\(\Leftrightarrow\left(x-23\right)\left(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\right)=0\)
\(\Leftrightarrow x-23=0\)( vì \(\frac{1}{24}+\frac{1}{25}-\frac{1}{26}-\frac{1}{27}\ne0\))
\(\Leftrightarrow x=23\)
Vậy nghiệm của pt x=23