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a) \(A=\dfrac{3737.43-4343.37}{2+4+6+...+2018}\)
\(\Leftrightarrow A=\dfrac{3737.43-43.101.37}{2+4+6+...+2018}\)
\(\Leftrightarrow A=\dfrac{3737.43-43.3737}{2+4+6+...+2018}\)
\(\Leftrightarrow A=\dfrac{0}{2+4+6+...+2018}\)
\(\Leftrightarrow A=0\)
b) \(B=\dfrac{101+100+99+...+3+2+1}{101-100+99-98+...+3-2+1}\)
\(\Leftrightarrow B=\dfrac{\left(101+1\right).101:2}{\left(101+99+97+...+1\right)-\left(100+98+96+...+2\right)}\)
\(\Leftrightarrow B=\dfrac{5151}{\left[\left(101+1\right).51:2\right]-\left[\left(100+2\right).50:2\right]}\)
\(\Leftrightarrow B=\dfrac{5151}{2601-2550}\)
\(\Leftrightarrow B=\dfrac{5151}{51}\)
\(\Leftrightarrow B=101\)
\(=\dfrac{8}{15}\left(\dfrac{33}{12}+\dfrac{33}{20}+\dfrac{33}{42}+\dfrac{33}{56}\right)\)
\(=\dfrac{8}{15}\cdot33\cdot\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\right)\)
\(=8\cdot\dfrac{11}{5}\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{8}\right)\)
\(=\dfrac{88}{5}\cdot\dfrac{7}{40}=\dfrac{77}{25}\)
25/53=25*101/53*101=2525/5353
25/53=25*1001/53*10101=252525/535353
=)25/53=2525/5353=252525/535353
y b) tuong tu nhe
duyet nha
A = \(\frac{3737x43-4343x37}{2+4+6+...+2018}\)
A = \(\frac{37x101x43-43x101x37}{2+4+6+..+2018}\)
A = \(\frac{0}{2+4+6+..+2018}\) = 0
a)\(\dfrac{3}{10}\)-x=\(\dfrac{25}{30}\)-\(\dfrac{4}{30}\)
\(\dfrac{3}{10}-x=\dfrac{7}{10}\)
x = \(\dfrac{3}{10}-\dfrac{7}{10}\)
x=\(\dfrac{-4}{10}\)
b)\(\dfrac{-5}{8}+x=\dfrac{4}{9}-\dfrac{63}{9}\)
\(\dfrac{-5}{9}+x=\dfrac{-59}{9}\)
\(x=\dfrac{-59}{9}-\dfrac{-5}{9}\)
\(x=\dfrac{-64}{9}\)
c)=>2.18=(x-3).(x-3)
=>36=(x-3)\(^2\)
=>6\(^2\)=(x-3)\(^2\)
6= x-3
x=6+3=9
1/ \(B=\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{8^2}\)
\(B< \dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{7.8}\)
\(B< \dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}\)
\(B< \dfrac{1}{1}-\dfrac{1}{8}< 1\)
\(B< 1\)
2/ \(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{20}\right)\)
\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{19}{20}\)
\(B=\dfrac{1\times2\times3\times...\times19}{2\times3\times4\times...\times20}\)
\(B=\dfrac{1}{20}\)
3/ \(A=\dfrac{7}{4}\cdot\left(\dfrac{3333}{1212}+\dfrac{3333}{2020}+\dfrac{3333}{3030}+\dfrac{3333}{4242}\right)\)
\(A=\dfrac{7}{4}\cdot\left(\dfrac{33}{12}+\dfrac{33}{20}+\dfrac{33}{30}+\dfrac{33}{42}\right)\)
\(A=\dfrac{7}{4}\cdot\left(\dfrac{33}{3.4}+\dfrac{33}{4.5}+\dfrac{33}{5.6}+\dfrac{33}{6.7}\right)\)
\(A=\dfrac{7}{4}.33.\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)
\(A=\dfrac{231}{4}.\left(\dfrac{1}{3}-\dfrac{1}{7}\right)\)
\(A=\dfrac{231}{4}\cdot\dfrac{4}{21}\)
\(A=11\)
4/ A phải là \(\dfrac{2011+2012}{2012+2013}\)
Ta có : \(B=\dfrac{2011}{2012}+\dfrac{2012}{2013}>\dfrac{2011}{2013}+\dfrac{2012}{2013}=\dfrac{2011+2012}{2013}>\dfrac{2011+2012}{2012+2013}=A\)
\(\Rightarrow B>A\)
7)\(\dfrac{-19}{34}\left(\dfrac{17}{19}+\dfrac{49}{18}\right)+\dfrac{49}{18}\left(\dfrac{19}{34}-\dfrac{18}{7}\right)\)
=\(\dfrac{-19}{34}.\dfrac{17}{19}+\dfrac{49}{18}.\dfrac{-19}{34}+\dfrac{49}{18}.\dfrac{19}{34}-\dfrac{18}{7}.\dfrac{49}{18}\)
=\(\dfrac{1}{2}+\left(\dfrac{49}{18}.\dfrac{-19}{34}+\dfrac{49}{18}.\dfrac{19}{34}\right)-7\)
=\(\dfrac{1}{2}+\left[\dfrac{49}{18}\left(\dfrac{-19}{34}+\dfrac{19}{34}\right)\right]-7\)
=\(\dfrac{1}{2}+0-7=\dfrac{-13}{2}\)
8)\(\dfrac{29}{32}\left(\dfrac{41}{36}-\dfrac{32}{58}\right)-\dfrac{41}{36}\left(\dfrac{29}{32}+\dfrac{18}{41}\right)\)
=\(\dfrac{29}{32}.\dfrac{41}{36}-\dfrac{29}{32}.\dfrac{32}{58}-\dfrac{41}{36}.\dfrac{29}{32}+\dfrac{18}{41}.\dfrac{41}{36}\)
=\(\left(\dfrac{29}{32}.\dfrac{41}{36}-\dfrac{41}{36}\dfrac{29}{32}\right)-\dfrac{29}{32}.\dfrac{32}{58}+\dfrac{18}{41}.\dfrac{41}{36}\)
=\(0-\dfrac{1}{2}+\dfrac{1}{2}=0\)
\(\frac{1313}{3737}=\frac{1313:101}{3737:101}=\frac{13}{37}\)
Ủng hộ mk nha
18.\(\left(\dfrac{3737}{4242}+\dfrac{3737}{5656}+\dfrac{3737}{7272}\right)\)
=18.\(\left(\dfrac{37}{42}+\dfrac{37}{56}+\dfrac{37}{72}\right)\)
=18.\(\dfrac{37}{18}\)
=37
`18 . (3737/4242+3737/5656+3737/7272)`
`=18. ( (37.101)/(42.101) + (37.101)/(56.101) + (37.101)/(72.101))`
`=18. (37/42+37/56 +37/72)`
`=18 . 37 . (1/42+1/56+1/72)`
`=18 . 37 . 1/18`
`=37`