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\(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}=0,368,..\) khi đem tu chia cho mau
1:2=0,5 CMR=0,5>0,368..
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)
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: \(\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3\)
\(=>\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{5}+3.\left(\frac{1}{12}+\frac{1}{60}\right)\)
\(=>\frac{1}{5}+\frac{1}{14}+\frac{1}{31}+\frac{1}{44}+\frac{1}{61}+\frac{1}{84}+\frac{1}{96}< \frac{1}{2}\)
\(=>Đpcm\)
1/5+1/14+1/27+1/43+1/61+1/89+1/111=0,368...( khi đem tử chia cho mẫu)
vi 1:2=0,5 ne 0,5>0,368...
CMR: 0,5>0,368..
nen 1/2 lon hon