Question

Chứng minh rằng \(S=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}

Answer 1

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)

Answer 2

Ta có:

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

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

Bài toán phụ 1:

Ta có:

1/13<1/12

1/14<1/12

1/15<1/12

=>1/13+1/14+1/15<1/12x3=1/4 (1)

Bài toán phụ 2:

Ta có:

1/61<1/60

1/62<1/60

1/63<1/60

=>1/61+1/62+1/63<1/60x3=1/20 (2)

Từ (1) và (2), ta có:

1/5+1/13+1/14+1/15+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<4/20+5/20+1/20

1/5+1/13+1/14+1/15+1/61+1/62+1/63<9/20<1/2

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