Question

\(S=\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+\frac{1}{24}+\frac{1}{25}+\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+\frac{1}{29}+\frac{1}{30}\)\(\frac{1}{30}\)

Hãy so sánh S với \(\frac{1}{3}\)

Answer 1

ta có 1/3=10/30

1/21+1/22+...+1/30 có 10 p/số

mà 1/21>1/30

1/22>1/30

....

1/29>1/30

1/30=1/30

=>1/21+..1/30>1/30+....1/30 có 10 phân số 

=>1/21+...1/30>1/3

Answer 2

Ta có: \(\frac{1}{21}< \frac{1}{30}\)

\(\frac{1}{22}< \frac{1}{30}\)

......

\(\frac{1}{29}< \frac{1}{30}\)

\(\Rightarrow S< \frac{1}{30}+\frac{1}{30}+...+\frac{1}{30}\)(có 10 p/s)
\(\Rightarrow S< \frac{1}{30}.10=\frac{10}{30}=\frac{1}{3}\)

Vậy S < 1/3

Answer 3

ta co 1/21+1/22+1/23>3/30

1/24+1/25+1/26>3/30

1/27+1/28+1/29>3/30

==>S>3/30+3/30+3/30+1/30

S>10/30 hay S>1/3