Question

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

Answer 1

\(\frac{1}{5}+\frac{1}{14}+\frac{1}{27}+\frac{1}{43}+\frac{1}{61}+\frac{1}{89}+\frac{1}{111}=0,368,..\) khi đem tu chia cho mau

1:2=0,5 CMR=0,5>0,368..

Answer 2

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)