CMR 1/41+1/42+1/43+...+1/79+7/80 <7/12
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Cmr 1/41+4/42+4/43+.........+1/79+1/80>7/12
Ta có:
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80
1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80)
Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60
và 1/61> 1/62> ... >1/79> 1/80
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80
Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12
=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12
=> ĐPCM
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Chứng minh 1/41 + 1/42 + 1/43 + ... + 1/79 + 1/80 > 7/12
Ta có:
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80
1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80)
Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60
và 1/61> 1/62> ... >1/79> 1/80
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80
Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12
=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12
=> ĐPCM
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Chứng minh:7/12< 1/41+1/42+1/43+...+1/79+1/80<1
A<10(1/40+1/50+1/70+1/60)=319/420<1
A>10(1/50+1/60+1/70+1/80)>7/12
=>7/12<A<1
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CM:1/41 + 1/42+1/43+...+1/79+1/80 >7/12
CMR:
\(\frac{7}{12}< \frac{1}{41}+\frac{1}{42}+\frac{1}{43}+.........+\frac{1}{79}+\frac{1}{80}< \frac{5}{6}\)
Đặt \(A=\frac{1}{41}+\frac{1}{42}+\frac{1}{43}+...+\frac{1}{79}+\frac{1}{80}\)
\(A>\frac{1}{80}+\frac{1}{80}+....+\frac{1}{80}\)
\(\frac{1}{80}+\frac{1}{80}+.....+\frac{1}{80}\\ =\frac{40}{80}=\frac{1}{2}\)
Vì \(\frac{1}{2}< \frac{5}{6}\\ =>A< \frac{5}{6}\)
\(A< \frac{1}{40}+\frac{1}{40}+.....+\frac{1}{40}\)
\(\frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}\\ =\frac{40}{40}=1\)
Vì \(1>\frac{7}{12}\\ =>A>\frac{7}{12}\)
bài này đề có vấn để
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chứng tỏ 1/41+1/42+1/43+.......+1/79+1/80>7/12
Tham khảo câu hỏi của Nguyễn Bá Thành ở ngay bên dưới
Chúc học giỏi !!!
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Chứng tỏ rằng: 1/41+1/42+1/43+...+1/79+1/80>7/12
Chứng minh rằng: 1/41+1/42+1/43+..........+1/79+1/80>7/12
chứng tỏ rằng :1 /41 +1/42 +1/43 +...+1/79+1/80 >7/12
Ta có:
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80
1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80)
Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60
và 1/61> 1/62> ... >1/79> 1/80
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80
Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12
=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12
=> ĐPCM
tk nha mk trả lời đầu tiên đó!!!
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A=1\41+1\42+1\43+...+1\79+1\80.chung minh A >7\12