Cho \(A=1\cdot3\cdot5\cdot7\cdot...\cdot49\)
\(B=\frac{1\cdot2\cdot3\cdot...\cdot48\cdot49\cdot50}{2\cdot4\cdot6\cdot...\cdot48\cdot50}\)
\(C=\frac{26}{2}\cdot\frac{27}{2}\cdot...\cdot\frac{50}{2}\)
So sánh A,B và C
Những câu hỏi liên quan
Tính Tổng :
\(A=\frac{1}{1\cdot2\cdot3\cdot4}+\frac{1}{2\cdot3\cdot4\cdot5}+\frac{1}{3\cdot4\cdot5\cdot6}+...+\frac{1}{47\cdot48\cdot49\cdot50}\) mọi người giúp em với ạ
\(A=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+....+\frac{1}{47.48.49.50}\)
\(=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{47.48.49}-\frac{1}{48.49.50}\right)\)
\(=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{48.49.50}\right)\)
\(=\frac{1}{3}.\frac{6533}{39200}=\frac{6533}{117600}\)
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Cho A=\(1\cdot3\cdot5\cdot7\cdot...\cdot49\)
B=\(\dfrac{26}{2}\cdot\dfrac{27}{2}\cdot...\cdot\dfrac{50}{2}\)
So sanhs A với B
Cho \(A=\frac{1\cdot3\cdot5\cdot...\cdot995\cdot997}{4\cdot6\cdot8\cdot...\cdot998\cdot1000};B=\frac{2\cdot4\cdot6\cdot...\cdot996\cdot998}{5\cdot7\cdot9\cdot...\cdot999\cdot1001}\)So sánh A và B
tinh
\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot...\cdot\frac{50^2}{49\cdot50}\)
\(\frac{2^2}{1.3}\times\frac{3^2}{2.4}\times............................\times\frac{50^2}{49.50}\)
\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times....................\times\frac{50.50}{49.50}\)
\(=\frac{\left(2.3.4..............50\right)\left(2.3.4............50\right)}{\left(1.2.3.............49\right)\left(3.4.5...........50\right)}\)
\(=\frac{50}{49}.2\)
\(=\frac{100}{49}\)
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\(\sqrt[2]{4\cdot9\frac{8}{8}+\frac{48\cdot11+5}{1\cdot\frac{814}{5+\frac{6145}{1\cdot\frac{821}{614}}}}}2548-\frac{8452}{14\cdot\frac{58}{96\cdot\frac{41}{\frac{24}{1\cdot\frac{975545}{1421+\frac{84874}{\frac{1+2+3+4+5+6+7+8+9\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{2\cdot\frac{2}{1}}}}}}}}\)
\(A=\frac{1\cdot2}{2\cdot2}\cdot\frac{2\cdot3}{3\cdot3}\cdot\frac{3\cdot4}{4\cdot4}\cdot\frac{4\cdot5}{5\cdot5}\cdot.................\cdot\frac{2012\cdot2013}{2013\cdot2013}\)với
\(B=\frac{2012\cdot2013-2012\cdot2012}{2012\cdot2011+2012\cdot2}\)
A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)
B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)
vậy A=B
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\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}.\frac{4.5}{5.5}.....\frac{2012.2013}{2013.2013}=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2012}{2013}=\frac{1.2.3.4.5....2012}{2.3.4.5....2013}=\frac{1}{2013}\)
\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}=\frac{2012.\left(2013-2012\right)}{2012.\left(2011+2\right)}=\frac{2012}{2012.2013}=\frac{1}{2013}\)
\(\Rightarrow A=B\)
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Bài 1:
a) \(\frac{1}{1}\cdot2+\frac{1}{2}\cdot3+\frac{1}{3}\cdot4+...+\frac{1}{n}\cdot\left(n+1\right)\)
b) \(\frac{1}{1}\cdot2\cdot3+\frac{1}{2}\cdot3\cdot4+\frac{1}{3}\cdot4\cdot5+...+\frac{1}{a}\cdot\left(a+1\right)\cdot\left(a+2\right)\)
b1:rút gọn
a) \(\frac{10\cdot11+50\cdot55+70\cdot77}{11\cdot12+55\cdot60+77\cdot84}\) b)\(\frac{1\cdot3\cdot5\cdot........\cdot49}{26\cdot27\cdot28\cdot......\cdot50}\)
\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^4}{3\cdot5}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)
\(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}=\frac{\left(1.2.3.4...50\right)^2}{1.2.3.4...50.51}=\frac{1.2.3...50}{51}=\frac{50!}{51}\)
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\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)
\(=\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\frac{5^2}{4\cdot6}\cdot\frac{7^2}{5\cdot7}\cdot\cdot\cdot\frac{50^2}{49\cdot51}\)
\(=\frac{2}{1}\cdot\frac{50}{51}=\frac{100}{51}\)
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\(A=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}...\frac{50^2}{49.51}\)
\(=\frac{2^2.3^2.4^2...49^2.50^2}{1.3.2.4.3.5...48.50.49.51}\)
\(=\frac{2.50}{1}=100\)
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