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https://olm.vn/hoi-dap/tim-kiem?q=+++++++++++Cho+s=5/20+5/21+5/22+5/23+...+5/49.ch%E1%BB%A9ng+minh+r%E1%BA%B1ng:+3+%3C+s+%3C+8&id=376641
tham khảo nhé bn
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(S=\frac{5}{20}+\frac{5}{21}+..........+\frac{5}{49}\)
\(=5\left(\frac{1}{20}+\frac{1}{21}+.......+\frac{1}{49}\right)\)
Mà \(\frac{1}{20}>\frac{1}{49};\frac{1}{21}>\frac{1}{49};.........;\frac{1}{49}=\frac{1}{49}\)
\(\Leftrightarrow5\left(\frac{1}{20}+\frac{1}{21}+.....+\frac{1}{49}\right)>5\left(\frac{1}{49}+\frac{1}{49}+.......+\frac{1}{49}\right)\)
\(\Leftrightarrow S>5.\frac{30}{49}\)
\(\Leftrightarrow S>3\frac{3}{49}\)
\(\Leftrightarrow S>3\left(1\right)\)
Lại có :
\(\frac{1}{20}=\frac{1}{20};\frac{1}{21}< \frac{1}{20};.......;\frac{1}{49}< \frac{1}{20}\)
\(\Leftrightarrow S=5\left(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{49}\right)< 5\left(\frac{1}{20}+\frac{1}{20}+....+\frac{1}{20}\right)\)
\(\Leftrightarrow S< 5.\frac{30}{20}=7\frac{1}{2}\)
\(\Leftrightarrow S< 8\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrow3< S< 8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=5.\left(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{49}\right)\)
Xét \(A=\frac{1}{20}+\frac{1}{21}+...+\frac{1}{49}\). Chứng minh 3/5 < A < 8/5
+ Có: \(\frac{1}{20}+\frac{1}{21}+...+\frac{1}{29}\frac{3}{5}\Rightarrow S>3\) (2)
Từ (1)(2) => 3 < S < 8
Này Trần Thị Loan à, tớ thấy cậu nên
thay chữ "xét" ở chỗ "xét A" thành chữ"đặt"
nghe hợp lý hơn.
![](https://rs.olm.vn/images/avt/0.png?1311)
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