Chứng tỏ :\(\frac{23}{34}<\frac{1}{31}+\frac{1}{32}+...+\frac{1}{70}<\frac{4}{3}\)
HL
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Chứng tỏ :\(\frac{23}{34}<\frac{1}{31}+\frac{1}{32}+...+\frac{1}{70}<\frac{4}{3}\)
Chứng tỏ rằng :\(\frac{23}{34}<\frac{1}{31}+\frac{1}{32}+...+\frac{1}{70}<\frac{4}{3}\)
Chứng tỏ :\(\frac{23}{34}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{70}<\frac{4}{3}\)
Chứng tỏ:
\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}.\frac{34}{2}....\frac{60}{2}=1.3.5....59\)
\(60!=1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot59\cdot60=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2\cdot4\cdot6\cdot...\cdot58\cdot60\)
\(=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\cdot1\cdot2\cdot3\cdot...\cdot30=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\times30!\)
\(\Rightarrow1\cdot3\cdot5\cdot...\cdot59=\frac{60!}{30!\times2^{30}}=\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}\)đpcm.
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\(\frac{31}{2}\cdot\frac{32}{2}\cdot...\cdot\frac{60}{2}\cdot2\cdot4\cdot...\cdot58\cdot60\)
=31.32.33.34...60.1.2.3.4.5...29.30
=1.2.3.4.5.6.7.8.9.10...60
1.3.5.7...59.2.4.6.8...60
=1.2.3.4.5.6...60
Vậy \(\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}=1\cdot3\cdot5\cdot...\cdot59\)
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Cho A= \(\frac{1}{1^2}+\frac{1}{2^3}+\frac{1}{3^4}+\frac{1}{4^5}+....+\frac{1}{99^{100}}\)
Chứng tỏ rằng A ko phải là số nguyên.
Chứng minh rằng :\(\frac{23}{34}<\frac{1}{31}+\frac{1}{32}+\frac{1}{33}+...+\frac{1}{70}<\frac{4}{3}\)
Chứng tỏ rằng:A=\(\frac{10}{27}\)+\(\frac{9}{16}\) +\(\frac{11}{34}\) <2
hãy chứng tỏ rằng những phân số sau đây bằng nhau: \(\frac{23}{99};\frac{2323}{9999};\frac{232323}{999999}\)
\(\frac{2323}{9999}=\frac{23.101}{99.101}=\frac{23}{99}\)
\(\frac{232323}{999999}=\frac{23.10101}{99.10101}=\frac{23}{99}\)
KL 3 phân số = nhau
Chứng tỏ rằng :
a) \(\frac{11}{15}<\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+...+\frac{1}{60}<\frac{3}{2}\)
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