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Cho S = 1/32 + 1/42 + 1/52 + ....... + 1/982 + 1/992 + 1/1002 . Chứng minh S < 1/2
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\(\frac{25-x}{18}=\frac{1}{2}\)
\(\frac{25-x}{18}=\frac{9}{18}\)
\(25-x=9\)
\(x=25-9\)
\(x=16\)
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\(\frac{25-x}{18}=\frac{1}{2}\)
\(\frac{25-x}{18}=\frac{9}{18}\)
\(25-x=9\)
\(x=25-9\)
\(x=16\)
\(\frac{25-x}{18}=\frac{1}{2}\)
\(\frac{25-x}{18}=\frac{9}{18}\)
\(\Rightarrow25-x=9\)
\(x=25-9\)
\(x=16\)
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Gọi số tiền của An là a, số tiền của Bình là b
Ta có:
a+b=560000 (1)
1/2a = 2/3 b => a= 4/3 b => a= 4/7 (a+b) (2)
Từ (1) và (2) ta có: a= 560000.4/7= 320000
b= 560000- 320000= 240000
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Ta có : \(2\frac{1}{3}-1\frac{1}{2}=\frac{7}{3}-\frac{3}{2}=\frac{14}{6}-\frac{9}{6}=\frac{5}{6}\)
Vì \(\frac{5}{6}=\frac{5}{6}\)
\(\Rightarrow2\frac{1}{3}-1\frac{1}{2}=\frac{5}{6}\)
k mk nha !
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{11.12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{1}-\frac{1}{12}\)
\(=\frac{11}{12}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{132}\)
\(A=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{11x12}\)
\(A=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+\frac{5-4}{4x5}+...+\frac{12-11}{11x12}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\)
\(A=1-\frac{1}{12}=\frac{11}{12}\)