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Tk mình đi mọi người mình bị âm nè!
Ai tk mình mình tk lại cho
Bài 1 :
a) 40/49 > 15/21
b) 22/49 > 3/8
c) 25/46 < 12/18
\(A=\frac{10^{2015}+1}{10^{2016}+1}\Rightarrow10A=\frac{10.\left(10^{2015}+1\right)}{10^{2016}+1}=\frac{10^{2016}+10}{10^{2016}+1}\)
\(A=\frac{10^{2016}+1+9}{10^{2016}+1}=\frac{10^{2016}+1}{10^{2016}+1}+\frac{9}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)
\(B=\frac{10^{2016}+1}{10^{2017}+1}\Rightarrow10B=\frac{10.\left(10^{2016}+1\right)}{10^{2017}+1}=\frac{10^{2017}+10}{10^{2017}+1}\)
\(B=\frac{10^{2017}+1+9}{10^{2017}+1}=\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)
Vì 102016+1 < 102017+1
=>\(\frac{9}{10^{2016}+1}>\frac{9}{10^{2017}+1}\)
=>\(1+\frac{9}{10^{2016}+1}>1+\frac{9}{10^{2017}+1}\)
=>10A > 10B
=>A > B
\(B=\frac{10^{2016}+1}{10^{2017}+1}<\frac{10^{2016}+1+9}{10^{2017}+1+9}\)
\(=\frac{10^{2016}+10}{10^{2017}+10}\)
\(=\frac{10.\left(10^{2015}+1\right)}{10.\left(10^{2016}+1\right)}\)
\(=\frac{10^{2015}+1}{10^{2016}+1}=A\)
\(\Rightarrow\) B<A
A,(2016*2017-1)/2015*2017+2016
=2015*2017+2016/2015*2017+2016
=1
B,18*(1919/2121+888/999)
=18*(19/21+8/9)
=18*(19/21)+18*(8/9)=114/7+16=16+2/7+16=32/2/7
c,gọi s=1/2+1/4+...+1/32
2s=1+1/2+...+1/16
2s-s=(1+1/2+...+1/16)-(1/2+1/4+...+1/32)
s=1-1/32=31/32