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

\(\Rightarrow S< \frac{1}{5}+\frac{1}{12}.3+\frac{1}{60}.3\)

\(\Rightarrow S< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}\)

\(\Rightarrow S< \frac{1}{2}\)

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)

S=1/5=(1/13+1/14+1/15)+(1/61+1/62+1/63)

suy ra S<1/5+1/12x3+1/60x3

S<1/5+1/4+1/20

=>S<1/2

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

Ta có:

S=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)<1/5+1/12.3+1/60.3

=>S<1/5+1/4+1/20=10/20

Hay S<1/2