CMR : \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
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CMR : \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
thách ai làm được
\(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}=0,368,..\) khi đem tu chia cho mau
1:2=0,5 CMR=0,5>0,368..
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ta có A=1/5+1/14+1/27+1/43+1/61+1/89+1/111
=1/5+(1/14+1/27+1/43)+(1/61+1/89+1/111)<1/5 +(1/12+1/12+1/12)+(1/60+1/60+1/60)=1/5+1/4+1/20=1/2
ta suy ra A<1/2(đpcm)
CMR :
A = \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
đố ai làm được
CMR :
A = \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
ĐỐ AI LÀM ĐƯỢC ! HA HA !
CMR : \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
THÁCH AI LÀM ĐƯỢC BÀI NÀY ! HA HA
CMR
A = \(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}<\frac{1}{2}\)
mau lên các bạn ơi mai mình phải nộp rồi
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
giải giúp mính nhé :
D\(=\) \(\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\)
CMR : D<\(\frac{1}{2}\)
A,TỪ LỚN ĐẾN BÉ
1,\(\frac{80}{79};\frac{29}{28};\frac{2013}{2012};\frac{112}{111}\)
B.TỪ BÉ ĐẾN LỚN
1.\(\frac{99}{100};\frac{61}{62};\frac{43}{45};\frac{15}{17}\)
2.\(\frac{27}{23};\frac{2010}{2007};\frac{71}{67};\frac{125}{121}\)
\(\frac{19}{28};\frac{80}{79};\frac{112}{111};\frac{2013}{2012}\)
\(\frac{99}{100};\frac{61}{62};\frac{43}{45};\frac{15}{17}\)
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chung minh rang:\(\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{2}\)
Ta có: \(\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}.\)
\(=\frac{1}{5}+\left(\frac{1}{14}+\frac{1}{31}+\frac{1}{44}\right)+\left(\frac{1}{61}+\frac{1}{84}+\frac{1}{96}\right)\)
Ta thấy \(\frac{1}{14}< \frac{1}{12}\)
\(\frac{1}{31}< \frac{1}{12}\)
\(\frac{1}{44}< \frac{1}{12}\)
\(=>\frac{1}{14}+\frac{1}{31}+\frac{1}{44}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}\)
\(=>\frac{1}{14}+\frac{1}{31}+\frac{1}{44}< \frac{1}{12}.3\left(1\right)\)
Ta lại thấy \(\frac{1}{61}< \frac{1}{60}\)
\(\frac{1}{84}< \frac{1}{60}\)
\(\frac{1}{96}< \frac{1}{60}\)
\(=>\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}\)
\(=>\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{60}.3\left(2\right)\)
Từ (1) và (2) suy ra: \(\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3\)
\(=>\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{5}+3.\left(\frac{1}{12}+\frac{1}{60}\right)\)
\(=>\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{2}\)
\(=>Đpcm\)
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