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\(\frac{6}{2.5}+\frac{6}{5.8}+\frac{6}{8.11}+...+\frac{6}{299.302}\)
\(=2\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+..+\frac{3}{299.302}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{299}-\frac{1}{302}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{302}\right)=2.\frac{75}{151}=\frac{150}{151}\)
\(A=\frac{54.107-53}{53.107+54}=\frac{\left(53+1\right).107-53}{53.107+54}\)
\(=\frac{53.107+107-53}{53.107+54}=\frac{53.107+54}{53.107+54}=1\)
\(B=\frac{135.269-133}{134.269+135}=\frac{\left(134+1\right)269-133}{134.269+135}\)
\(=\frac{134.269+269-133}{134.269+135}=\frac{134.269+136}{134.269+135}>1\)
\(\Rightarrow B>A\)
\(A=10^{30}=\left(10^3\right)^{10}=1000^{10}\)
\(B=2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
Do: 1000 < 1024 nên 100010 < 102410
Hay: A < B
NHO GIAI RA DAY DU NHA!
a,C=(35+2).57-14
=35.57+2.57-14
=35.57+114-14
=35.57+100
suy ra c>d
b,E=199.(200+1)
=199.1+199.200
=199+199.200
F=200.(199+1)
= 200.1+200.199
=200+200.199
suy ra F>E
c, N= 2000+b.10+c+d.10+4+a.100+c
=(2000+4)+(a.100+b.10+c)+(d.10+c)
=2004+abc+dc
Vi 2004<2014 nen M>N
t i c k ho minh cai nha t i c k co mat cai gi dau