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Ta có:
\(\frac{9}{7}=\frac{9\times5}{7\times5}=\frac{45}{35}\)
Vì \(\frac{46}{35}>\frac{45}{35}\)
Nên \(\frac{46}{35}>\frac{9}{7}\)
* Quy đồng : 9/7 = 45/ 35
Ta thấy 46> 45 => 46/35 > 45/35
Hay 46/35> 9/7
![](https://rs.olm.vn/images/avt/0.png?1311)
a)Ta có:A:B=\(\left(\frac{1}{4}.\frac{3}{6}.\frac{5}{8}....\frac{43}{46}.\frac{45}{48}\right):\left(\frac{2}{5}.\frac{4}{7}.\frac{6}{9}....\frac{44}{47}.\frac{46}{49}\right)=\frac{\left(1.3.5...45\right).\left(2.4.6...46\right)}{\left(4.6.8...48\right)\left(5.7.9...49\right)}=\frac{3.2}{47.48.49}
![](https://rs.olm.vn/images/avt/0.png?1311)
\(M=\frac{1}{2}-\frac{1}{2^4}+\frac{1}{2^7}-\frac{1}{2^{10}}+....+\frac{1}{2^{43}}-\frac{1}{2^{46}}+\frac{1}{2^{49}}-\frac{1}{2^{52}}\)
Nên \(2^3.M=4-\frac{1}{2}+\frac{1}{2^4}-\frac{1}{2^7}+.....+\frac{1}{2^{46}}-\frac{1}{2^{52}}\)
Suy ra \(2^3.M-M=4-\frac{1}{2^{52}}\)hay\(7.M=4-\frac{1}{2^{52}}\).
Khi đó \(M=\frac{4}{7}-\frac{1}{2^{52}.7}< 1\)
Vì \(\frac{9}{4}>1;M< 1\)nên \(\frac{9}{4}>M\)
Vậy \(\frac{9}{4}>M\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có : (1/35)^7 giữ nguyên
(1/15)^9=[(1/15)^2]^7=(1/3375)^7
vì ^7=^7 . Mà 35<3375 =>1/35>1/3375
=>(1/35)^7>(1/3375)^7 => (1/35)^7>(1/15)^9
Vậy (1/35)^7>(1/15)^9
![](https://rs.olm.vn/images/avt/0.png?1311)
d, ta có :(-32)9=-(329) ;(-18)13=-(1813)
329=32\(\times\)328=32\(\times\)(322)4=32\(\times\)10244=32\(\times\)1024\(\times\)10243
1813=18\(\times\)1812=18\(\times\)(183)4=18\(\times\)58324=18\(\times\)5832\(\times\)58323
18\(\times\)5832 >16\(\times\)5832=32\(\times\)2916>32\(\times\)1024 =58323>10243
nên 1813>329
vậy (-18)13 <(-32)9
(-32)9=-(329)
(-18)13=-(1813)
329<369
ta có :369=(2\(\times\)18)9=29\(\times\)189
vì 184>164mà 164=(24)4=216
mà 216>29
\(\Rightarrow\)184>29
\(\Rightarrow\)184\(\times\)189>29\(\times\)189
\(\Rightarrow\)1813>369mà 369 >329
\(\Rightarrow\)1813>329
\(\Rightarrow\)(-18)13<(-32)9
Ta có:\(\frac{9}{7}=\frac{45}{35}\)
Vì: \(\frac{45}{35}< \frac{46}{35}\)
Vậy: \(\frac{46}{25}>\frac{9}{7}\)
\(Tacó:\)
\(\frac{9}{7}=\frac{9.5}{7.5}=\frac{45}{35}\)
Vì \(\frac{46}{35}>\frac{45}{35}\)
Nên \(\frac{46}{35}>\frac{9}{7}\)