\(ChoM=\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}.\)
Chứng tỏ rằng 1<M<2
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25 phần 24 , 19 phần 18 , 21 phần 20 , 24 phần 23 , 18 phần 17
\(\dfrac{1}{21}+\dfrac{2}{21}+\dfrac{3}{21}+\dfrac{4}{21}+\dfrac{5}{21}+...+\dfrac{17}{21}+\dfrac{18}{21}+\dfrac{19}{21}+\dfrac{20}{21}\)
\(=\dfrac{1+2+3+4+5+...+17+18+19+20}{21}\)
\(=\dfrac{1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20}{21}\)
\(=\dfrac{210}{21}\)
\(=10\)
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