Ta thấy:
1/3 < 1/2 = 1 - 1/2
1/7 = 1/(3x2 + 1) < 1/(3x2) = 1/2 - 1/3
1/13 = 1/(3x4 + 1) < 1/(3x4) = 1/3 - 1/4
1/21 = 1/(4x5 + 1) < 1/(4x5) = 1/4 - 1/5
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1/73 = 1/(8x9 + 1) < 1/(8x9) = 1/8 - 1/9
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Cộng tất cả lại :
1/3 + 1/7 + 1/13 + 1/21 +...+ 1/73 + ... < (1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ....+ (1/8 - 1/9) + ...< 1
Đặt \(A=\frac{1}{3}+\frac{1}{7}+\frac{1}{13}+.....+\frac{1}{91}\)
Ta có: \(A< \frac{1}{2}+\frac{1}{6}+\frac{1}{12}+.....+\frac{1}{90}\)
\(\Rightarrow A< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{9.10}\)
\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+........+\frac{1}{9}-\frac{1}{10}\)
\(\Rightarrow A< 1-\frac{1}{10}\)
\(\Rightarrow A< \frac{9}{10}\)
Vì \(A< \frac{9}{10}< 1\Rightarrow A< 1\RightarrowĐPCM\)
câu này làm nnhuw thế nào 7/12<1/41+1/42+1/43+...+1/9+1/80<1
ta co: 1/3 <1/2 1/7<1/6 1/13< 1/12 1/21<1/20 1/31<1/30 1/43< 1/42+.....+ 1/91<1/90
1/2+1/6+1/12+ 1/20+ 1/30+1/42+.........+ 1/90.
1/1x2+ 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 +.........+ 1/9x10<1
1-1/2+1/3-1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7+...........+1/9-1/10<1
1-1/9<1
chung minh rang 1/3 +1/7+ 1/13 + 1/21+ 1/42+....+1/91<1
Mục tiêu -1000 sp nha xin đc giúp đỡ
Yêu cầu đừng có khóa nick nha
cái quần què dì dạy
