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a: \(\dfrac{25}{26}=1-\dfrac{1}{26}\)
\(\dfrac{50}{51}=1-\dfrac{1}{51}\)
mà \(-\dfrac{1}{26}< -\dfrac{1}{51}\)
nên \(\dfrac{25}{26}< \dfrac{50}{51}\)
b: \(\dfrac{149}{157}=1-\dfrac{8}{157}\)
\(\dfrac{449}{457}=1-\dfrac{8}{457}\)
mà \(-\dfrac{8}{157}>-\dfrac{8}{457}\)
nên \(\dfrac{149}{157}>\dfrac{449}{457}\)
a) \(\frac{25}{26}=\frac{50}{52}\) b) \(\frac{51}{58}< \frac{61}{68}\) c) \(\frac{101}{506}< \frac{707}{3534}\)
c) Đặt \(A=2^0+2^1+2^2+...+2^{50}\)
\(\Leftrightarrow2A=2^1+2^2+2^3...+2^{51}\)
\(\Leftrightarrow2A-A=2^1+2^2+2^3...+2^{51}\)\(-2^0-2^1-2^2-...-2^{50}\)
\(\Leftrightarrow A=2^{51}-2^0=2^{51}-1< 2^{51}\)
Vậy \(2^0+2^1+2^2+...+2^{50}< 2^{51}\)
a)Ta có: \(\hept{\begin{cases}2^{30}=\left(2^3\right)^{10}=8^{10}\\3^{30}=\left(3^3\right)^{10}=27^{10}\\4^{30}=\left(2^2\right)^{30}=2^{60}\end{cases}}\)và \(\hept{\begin{cases}3^{20}=\left(3^2\right)^{10}=9^{10}\\6^{20}=\left(6^2\right)^{10}=36^{10}\\8^{20}=\left(2^3\right)^{20}=2^{60}\end{cases}}\)
Mà \(8^{10}< 9^{10}\); \(27^{10}< 36^{10}\);\(2^{60}=2^{60}\)nên
\(8^{10}+27^{10}+2^{60}< 9^{10}+36^{10}+2^{60}\)
hay \(2^{30}+3^{30}+4^{30}< 3^{20}+6^{20}+8^{20}\)
a) 3200=(32)100=9100 ; 2300=(23)100=8100
=> 9100>8100 hay 3200>2300
b) 7150=(712)25=504125 ; 3775=(373)25=5065325
=> 504125<5065325 hay 7150<3775
c)rút gọn
2016014/2017015=2014/2015
2016016014/2017017015=2014/2015
=> 2014/2015 = 2014/2015
\(\dfrac{51}{50};\dfrac{27}{26};\dfrac{25}{24};\dfrac{18}{17};\dfrac{4}{3}\)
\(\dfrac{51}{50}< \dfrac{27}{26}< \dfrac{25}{24}< \dfrac{26}{25}< \dfrac{18}{17}< \dfrac{4}{3}\)
\(\Leftrightarrow\frac{25}{48}.2=\frac{34}{69}.2\)
\(\Leftrightarrow\frac{25}{24}\text{và}\frac{68}{69}\)
mà\(\frac{25}{24}>1\)
\(\frac{68}{69}< 1\)
\(\Rightarrow\frac{25}{24}>\frac{68}{69}\)
\(\Rightarrow\frac{25}{48}>\frac{34}{69}\)
a)-17/24 > -25/31
b)-27/38 < -125/195
c)-22/111> -27/134
nhớ k nha!!!!!!!!!!!!!!!!!!
lấy phân số trung gian
có \(\frac{27}{39}>\frac{27}{41}\) (1)
\(\frac{26}{41}\frac{27}{41}>\frac{26}{41}\) hay \(\frac{27}{39}>\frac{26}{41}\)
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**** cho mình nha bnKhánh Linh
a ) X é t 1 − 25 26 = 1 26 ; 1 − 50 51 = 1 51 . V ì 1 26 > 1 51 = > 25 26 < 50 51
b ) X é t 1 − 213 321 = 108 321 ; 1 − 105 213 = 108 213 . V ì 108 321 < 108 213 = > 213 321 > 105 213
c ) X é t 1 + − 99 100 = 1 100 ; 1 + − 21 22 = 1 22 . V ì 1 100 < 1 11 = > − 99 100 > − 21 22 d ) X é t 1 + − 124 129 = 5 129 ; 1 + − 132 137 = 5 137 . V ì 5 129 > 5 137 = > − 124 129 > − 132 137