19-18
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Có \(\frac{18}{18+19+20}>\frac{18}{18+19+20+21}\)
\(\frac{19}{18+19+21}>\frac{19}{18+19+20+21}\)
\(\frac{20}{18+19+21}>\frac{20}{18+19+20+21}\)
\(\frac{21}{18+19+21}>\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18}{18+19+20+21}+\frac{19}{18+19+20+21}+\frac{20}{18+19+20+21}+\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18+19+20+21}{18+19+20+21}\)
=>\(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>1\)
=>M>1
Còn lại mình không biết, đúng thì tick nha
17 (18 + 19) + 12 (18 + 19) - 18 - 19
17.37+12.37-18-19
37.(17+12)-18-19
37.29-18-19
1073-18-19
1066-19
1036
k nhé
.................xoxo................
\(\frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2\)
\(=\left(\frac{11}{19}+\frac{8}{19}\right)+\left(\frac{19}{18}-\frac{1}{18}\right)+5,2\)
\(=1+1+5,2\)
\(=7,2\)
\(\frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2\)
\(=\left(\frac{11}{19}+\frac{8}{19}\right)+\left(\frac{19}{18}-\frac{1}{18}\right)+5,2\)
\(=\frac{19}{19}+\frac{18}{18}+5,2\)
\(=1+1+5,2=7,2\)
Ta có công thức :
\(\frac{a}{b}< \frac{a+c}{b+c}\)\(\left(a,b,c\inℕ^∗\right)\)
Áp dụng vào ta có :
\(A=\frac{19^{18}+1}{19^{19}+1}< \frac{19^{18}+1+18}{19^{19}+1+18}=\frac{19^{18}+19}{19^{19}+19}=\frac{19\left(19^{17}+1\right)}{19\left(19^{18}+1\right)}=\frac{19^{17}+1}{19^{18}+1}=B\)
\(\Rightarrow\)\(A< B\) ( đpcm )
Vậy \(A< B\)
Chúc bạn học tốt ~
\(\dfrac{9}{14}+\dfrac{19}{18}+\dfrac{19}{14}+\dfrac{35}{18}=\left(\dfrac{9}{14}+\dfrac{19}{14}\right)+\left(\dfrac{19}{18}+\dfrac{35}{18}\right)=\dfrac{28}{14}+\dfrac{54}{18}=2+3=5\)
\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{\dfrac{19}{1}+\dfrac{18}{2}+\dfrac{17}{3}+....+\dfrac{1}{19}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{20}}{1+\left(\dfrac{18}{2}+1\right)+\left(\dfrac{17}{3}+1\right)+\left(\dfrac{1}{19}+1\right)}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{1+\dfrac{20}{2}+\dfrac{20}{3}+...+\dfrac{20}{19}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{20}}{20.\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{19}+\dfrac{1}{20}\right)}\)
\(=\dfrac{1}{20}\)
mình ghi sai đáng nhẽ là 19-18=1
19-18=1 nhé