\(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{19}+\frac{1}{20}+\frac{1}{21}>\frac{5}{11}\)
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Tính giá trị biểu thức1.Afrac{1}{5}+frac{3}{17}-frac{4}{3}+left(frac{4}{5}-frac{3}{17}+frac{1}{3}right)-frac{1}{7}+left[frac{-14}{30}right]2.Bleft(frac{5}{8}-frac{4}{12}+frac{3}{2}right)-left(frac{5}{8}+frac{9}{13}right)-left[frac{-3}{2}right]+frac{7}{-15}3.Cfrac{5}{18}+frac{8}{19}-frac{7}{21}+left(frac{-10}{36}+frac{11}{19}+frac{1}{3}right)-frac{5}{8}4.Dfrac{1}{9}-left[frac{-5}{23}right]-left(frac{-5}{23}+frac{1}{9}+frac{25}{7}right)+frac{50}{14}-frac{7}{30}5.Efrac{1}{13}+left(frac{-5}{18}-frac...
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Tính giá trị biểu thức
\(1.A=\frac{1}{5}+\frac{3}{17}-\frac{4}{3}+\left(\frac{4}{5}-\frac{3}{17}+\frac{1}{3}\right)-\frac{1}{7}+\left[\frac{-14}{30}\right]\)
\(2.B=\left(\frac{5}{8}-\frac{4}{12}+\frac{3}{2}\right)-\left(\frac{5}{8}+\frac{9}{13}\right)-\left[\frac{-3}{2}\right]+\frac{7}{-15}\)
\(3.C=\frac{5}{18}+\frac{8}{19}-\frac{7}{21}+\left(\frac{-10}{36}+\frac{11}{19}+\frac{1}{3}\right)-\frac{5}{8}\)
\(4.D=\frac{1}{9}-\left[\frac{-5}{23}\right]-\left(\frac{-5}{23}+\frac{1}{9}+\frac{25}{7}\right)+\frac{50}{14}-\frac{7}{30}\)
\(5.E=\frac{1}{13}+\left(\frac{-5}{18}-\frac{1}{13}+\frac{12}{17}\right)+\left(\frac{12}{17}+\frac{5}{18}+\frac{7}{5}\right)\)
\(6.F=\frac{15}{14}-\left(\frac{17}{23}-\frac{80}{87}+\frac{5}{4}\right)+\left(\frac{12}{17}-\frac{15}{14}+\frac{1}{4}\right)\)
\(7.G=\frac{1}{25}-\frac{4}{27}+\left(\frac{-23}{27}+\frac{-1}{25}-\frac{5}{43}\right)+\frac{5}{43}-\frac{4}{7}\)
\(8.H=\frac{4}{15}-\frac{23}{28}-\left(\frac{-23}{28}+\frac{-11}{15}-\frac{29}{27}\right)-\frac{2}{27}\)
\(9.K=\frac{1}{16}-\frac{5}{21}+\left(\frac{-1}{16}+\frac{-3}{5}-\frac{-5}{21}\right)+\frac{-2}{5}+\frac{3}{4}\)
\(10.L=\frac{7}{12}+\frac{15}{14}-\left(\frac{14}{22}+\frac{-1}{14}+\frac{5}{21}\right)-\frac{-5}{21}+\frac{3}{5}\)
yutyugubhujyikiu
Thực hiện so sánh:\(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}\)\(+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}+\frac{1}{21}+\frac{1}{22}\)\(+\frac{1}{23}\)với \(\frac{5}{6}\)
Đặt S=1/12+1/13+1/14+1/15+...+1/23
ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)
đặt A=1/12+1/13+1/14+...+1/17
ta có
1/13<1/12
1/14<1/12
..........................
.........................
1/17<1/12
=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)
=>A<1x6/12
=>A<1/2 (1)
Đặt B=1/18+1/19+...+11/23
ta có
1/19<1/18
1/20<1/18
...........................
..........................
1/23<1/18
=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)
=>B<1x 6/18
=>B<1/3 (2)
từ 1 và 2 =>S=A+B<1/2+1/3
=>S<5/6 (dpcm)
k cho mình nhé
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Đặt S=1/12+1/13+1/14+1/15+...+1/23
ta có 1/12+1/13+1/14+1/15+...+1/22+1/23 = (1/12+1/13+1/14+...+1/17)+(1/18+1/19+...+1/23)
đặt A=1/12+1/13+1/14+...+1/17
ta có
1/13<1/12
1/14<1/12
..........................
.........................
1/17<1/12
=>A<1/12+1/12+1/12+....+1/12 (có 6 phân số)
=>A<1x6/12
=>A<1/2 (1)
Đặt B=1/18+1/19+...+11/23
ta có
1/19<1/18
1/20<1/18
...........................
..........................
1/23<1/18
=> B<1/18+1/18+1/18+...+1/18 (có 6 phân số)
=>B<1x 6/18
=>B<1/3 (2)
từ 1 và 2 =>S=A+B<1/2+1/3
=>S<5/6 (dpcm)
k cho mình nhé
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C/m ::
\(S=\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}+\frac{1}{21}+\frac{1}{22}>\frac{1}{2}\)
Cho S= \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)
So sánh S với \(\frac{1}{2}\)
mình học toán cảm thấy nhức óc lắm, hoa mắt luôn 
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Ta thấy:
1/11<1/4
1/12<1/4
.......
1/20<1/4
Suy ra ta có:
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Vì \(\dfrac{1}{11}>\dfrac{1}{20};\dfrac{1}{12}>\dfrac{1}{20};....;\dfrac{1}{19}>\dfrac{1}{20};\dfrac{1}{20}=\dfrac{1}{20}\)
\(\Rightarrow s>\dfrac{1}{20}+\dfrac{1}{20}+\dfrac{1}{20}.........+\dfrac{1}{20}\)(20 phân số)
\(\Rightarrow S>\dfrac{10}{20}=\dfrac{1}{2}\)
Vậy \(S>\dfrac{1}{2}\)
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Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
Ta xét : \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{20}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+....+\frac{1}{20}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)\)
\(=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\)
Vì \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
nên \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\) ( đpcm )
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\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)
Hãy so sánh S và \(\frac{1}{2}\)
\(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+....+\frac{1}{20}\)
\(=\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)\)
\(>\frac{1}{15}\cdot5+\frac{1}{20}\cdot5\)
\(=\frac{1}{3}+\frac{1}{4}\)
\(=\frac{7}{12}>\frac{6}{12}=\frac{1}{2}\)
\(\Rightarrow S>\frac{1}{2}\)
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Bài làm
Ta có:
\(\frac{1}{11}>\frac{1}{20}\), \(\frac{1}{12}>\frac{1}{20}\), \(\frac{1}{13}>\frac{1}{20}\), \(\frac{1}{14}>\frac{1}{20}\), \(\frac{1}{15}>\frac{1}{20}\), \(\frac{1}{16}>\frac{1}{20}\), \(\frac{1}{17}>\frac{1}{20}\), \(\frac{1}{18}>\frac{1}{20}\),\(\frac{1}{19}>\frac{1}{20}\)
=> \(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}\)
hay \(\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}\)
=> \(S=\frac{1}{20}.10=\frac{10}{20}=\frac{1}{2}\)
Do đó: \(S=\frac{1}{2}\)
# Chúc bạn học tốt #
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Ta có các phân số : \(\frac{1}{11};\frac{1}{12};\frac{1}{13};\frac{1}{14};\frac{1}{15};\frac{1}{16};\frac{1}{17};\frac{1}{18};\frac{1}{19}>\frac{1}{20}\)
Do đó : \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)có 10 phân số \(\frac{1}{20}\)
\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{10}{20}\)
\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{2}\)
Vậy : \(S>\frac{1}{2}\)
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Bài 1: Tính
frac{3}{8}.19frac{1}{3}-frac{3}{8}.33frac{1}{3}
1frac{4}{23}+frac{5}{21}-frac{4}{23}+0,5+frac{16}{21}
frac{21}{47}+frac{9}{45}+frac{26}{47}+frac{4}{5}
frac{15}{12}+frac{5}{13}-frac{3}{12}-frac{18}{13}
frac{11}{24}-frac{5}{41}+frac{13}{24}+0,5-frac{36}{41}
left(-frac{3}{4}+frac{2}{3}right):frac{5}{11}+left(-frac{1}{4}+frac{1}{3}right):frac{5}{11}
left(-3right)^2.left(frac{3}{4}-0,25right)-left(3frac{1}{2}-1frac{1}{2}right)
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Bài 1: Tính
\(\frac{3}{8}.19\frac{1}{3}-\frac{3}{8}.33\frac{1}{3}\)
\(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
\(\frac{21}{47}+\frac{9}{45}+\frac{26}{47}+\frac{4}{5}\)
\(\frac{15}{12}+\frac{5}{13}-\frac{3}{12}-\frac{18}{13}\)
\(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)
\(\left(-\frac{3}{4}+\frac{2}{3}\right):\frac{5}{11}+\left(-\frac{1}{4}+\frac{1}{3}\right):\frac{5}{11}\)
\(\left(-3\right)^2.\left(\frac{3}{4}-0,25\right)-\left(3\frac{1}{2}-1\frac{1}{2}\right)\)
Cho \(S=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\)
Hãy so sánh S với \(\frac{1}{2}\)
bài 1:thực hiện phép tính : a)frac{3}{7}+frac{5}{13}+frac{4}{13}b)left(frac{3}{8}+frac{-3}{4}+frac{7}{12}right):frac{5}{6}+frac{1}{2}c)frac{2}{5}.frac{1}{3}-frac{2}{15}:frac{1}{5}+frac{3}{5}.frac{1}{3}d)left(4-frac{5}{12}right):2+frac{5}{24}e)frac{7}{19}.frac{8}{11}+frac{3}{11}.frac{7}{19}+frac{-1}{19}f)frac{9}{27}+frac{8}{24}+frac{18}{27}-frac{-16}{24}+frac{2}{3}g)frac{-5}{21}+frac{-2}{21}+frac{8}{24}h)frac{-5}{9}+frac{8}{15}+frac{-2}{11}+frac{4}{-9}+frac{7}{15}i)frac{7}{25}.frac{39}{-14}.frac{...
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bài 1:thực hiện phép tính :
a)\(\frac{3}{7}+\frac{5}{13}+\frac{4}{13}\)
b)\(\left(\frac{3}{8}+\frac{-3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
c)\(\frac{2}{5}.\frac{1}{3}-\frac{2}{15}:\frac{1}{5}+\frac{3}{5}.\frac{1}{3}\)
d)\(\left(4-\frac{5}{12}\right):2+\frac{5}{24}\)
e)\(\frac{7}{19}.\frac{8}{11}+\frac{3}{11}.\frac{7}{19}+\frac{-1}{19}\)
f)\(\frac{9}{27}+\frac{8}{24}+\frac{18}{27}-\frac{-16}{24}+\frac{2}{3}\)
g)\(\frac{-5}{21}+\frac{-2}{21}+\frac{8}{24}\)
h)\(\frac{-5}{9}+\frac{8}{15}+\frac{-2}{11}+\frac{4}{-9}+\frac{7}{15}\)
i)\(\frac{7}{25}.\frac{39}{-14}.\frac{50}{78}\)
m.n làm nhanh cho mình nhé, chiều mình phải nộp rồi! cảm ơn m.n!