gọi đó là A đi.

Ta có:

1/13+1/14+1/14< 1/12+1/12+1/12=3/12=1/4

1/61+1/62+1/63< 1/60+1/60+1/60=3/60=1/20

=> 1/5+1/13+1/14+1/15+1/61+1/62+1/63<1/5+1/4+1/20=1/2

=>A< 1/2 (ĐPCM)

Ta có : 

S = \(\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)

TA có:

1/12>1/13

1/12>1/14

1/12>1/15

=>1/12.3=1/4>1/13+1/14+1/15

1/60>1/61

1/60>1/62

1/60>1/63

=>1/60.3=1/20>1/61+1/62+1/63

=>1/5+1/4+1/20> 1/5+1/13+1/14+1/15+1/61+1/62+1/63

=>1/2> 1/5+1/13+1/14+1/15+1/61+1/62+1/63

Ta có: 

\(\frac{1}{5}=\frac{1}{5}\)

\(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}

Ta có: \(S=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)

\(đpcm\Leftrightarrow\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}