Question

[Trần Thùy Linh A1]

Cho S= 1/11 + 1/12 + 1/13 +.....+ 1/20

CMR:1/2 < S <1

Answer 1

[nguyễn thị thúy vy]

lớp mấy vay

Answer 2

[Lê Chí Cường]

Ta thấy: \(\frac{1}{11}>\frac{1}{20}\)

\(\frac{1}{12}>\frac{1}{20}\)

\(\frac{1}{13}>\frac{1}{20}\)

................

\(\frac{1}{19}>\frac{1}{20}\)

=>\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}+\frac{1}{20}\)

=>\(S>\frac{10}{20}\)

=>\(S>\frac{1}{2}\)(1)

Lại có: 

\(\frac{1}{11}<\frac{1}{10}\)

\(\frac{1}{12}<\frac{1}{10}\)

\(\frac{1}{13}<\frac{1}{10}\)

................

\(\frac{1}{20}<\frac{1}{10}\)

=>\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}<\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)

=>\(S<\frac{10}{10}\)

=>S<1 (2)

Từ (1) và (2)

=>1/2<S<1

=>ĐPCM