tính nhanh
\(\left(\frac{1}{10}-1\right).\left(\frac{1}{11}-1\right).\left(\frac{1}{12}-1\right)....\left(\frac{1}{2012}-1\right)\)
Những câu hỏi liên quan
Tính: A=\(\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)
A= ( 1/10-1) + ( 1/11 - 1 ) +...+ ( 1/100-1)
= 9/10 + 10/11 +...+ 99/100
= 9/100
^_^ ( have a good day)
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23 tháng 8 2016 lúc 10:43
Tính : \(\frac{\left(1^4+\frac{1}{4}\right)\left(3^4+\frac{1}{4}\right)\left(5^4+\frac{1}{4}\right)\left(7^4+\frac{1}{4}\right)\left(9^4+\frac{1}{4}\right)\left(11^4+\frac{1}{4}\right)}{\left(2^4+\frac{1}{4}\right)\left(4^4+\frac{1}{4}\right)\left(6^4+\frac{1}{4}\right)\left(8^4+\frac{1}{4}\right)\left(10^4+\frac{1}{4}\right)\left(12^4+\frac{1}{4}\right)}\)
tính nhanh \(\left(-1\frac{1}{3}\right).\left(-1\frac{1}{4}\right).\left(-1\frac{1}{5}\right)....\left(-1\frac{1}{2012}\right)\)
\(\left(-1\frac{1}{3}\right).\left(-1\frac{1}{4}\right).\left(-1\frac{1}{5}\right)....\left(-1\frac{1}{2012}\right)=\frac{-2}{3}.\frac{-3}{4}.....\frac{-2011}{2012}=\frac{2}{2012}=\frac{1}{1006}\)
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hình như có chỗ nhầm:
\(=\frac{-4}{3}\cdot\frac{-5}{4}\cdot\frac{-6}{5}\cdot...\cdot\frac{-2013}{2012}\)
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Tính nhanh :
(5+10+15+....+1000)+\(\left(\frac{2}{5}:0,5+2.\left(-0,4\right)\right):\left(\frac{1}{5}+\frac{1}{10}+....+\frac{1}{2012}\right)\)
tính
a, \(\frac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}\)
b , \(\left(\frac{0,4-\frac{8}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\right):\frac{2012}{2013}\)
c, A
= \(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+...+\frac{1}{20}.\left(1+2+3+....+20\right)\right).155\)
\(a,\frac{16^3.3^{10}+120.6^9}{4^6.3^{12}+6^{11}}\)
\(=\frac{\left(2^4\right)^3.3^{10}+2^3.3.5.\left(2.3\right)^9}{\left(2^2\right)^6.3^{12}+\left(2.3\right)^{11}}\)
\(=\frac{2^{12}.3^{10}+2^3.3.5.2^9.3^9}{2^{12}.3^{12}+2^{11}.3^{11}}\)
\(=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3+1\right)}\)
\(=\frac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.7}=\frac{2.6}{3.7}=\frac{4}{7}\)
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\(D=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)
\(\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{99}-1\right)\left(\frac{1}{100}-1\right)\)
\(=-\frac{9}{10}.\frac{-10}{11}.\frac{-11}{12}...\frac{-99}{100}\)
\(=-\frac{9}{100}\)
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Thực hiện phép tính :a, sqrt{12frac{1}{4}}.left(-frac{2}{7}right)^2-left[2,left(4right).2frac{5}{11}right]:(-frac{42}{5})b, left(1-frac{1}{2}right).left(1-frac{1}{3}right).left(1-frac{1}{4}right)...left(1-frac{1}{2007}right)c, frac{0,375-0,3+frac{3}{11}+frac{3}{12}}{-0,625+0,5-frac{5}{11}-frac{5}{12}}+frac{1,5+1-0,75}{2,5+frac{5}{3}-1,25}Các bạn giải nhanh giúp mình nha!
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Thực hiện phép tính :
a, \(\sqrt{12\frac{1}{4}}.\left(-\frac{2}{7}\right)^2-\left[2,\left(4\right).2\frac{5}{11}\right]:(-\frac{42}{5})\)
b, \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2007}\right)\)
c, \(\frac{0,375-0,3+\frac{3}{11}+\frac{3}{12}}{-0,625+0,5-\frac{5}{11}-\frac{5}{12}}+\frac{1,5+1-0,75}{2,5+\frac{5}{3}-1,25}\)
Các bạn giải nhanh giúp mình nha!
\(A=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)\left(\frac{1}{12}-1\right)...\left(\frac{1}{100}-1\right)\)
\(=\frac{-9}{10}\cdot\frac{-10}{11}\cdot\frac{-11}{12}\cdot\cdot\cdot\cdot\frac{-99}{100}\)
\(=\frac{9}{-10}\cdot\frac{-10}{11}\cdot\frac{11}{-12}\cdot\cdot\cdot\cdot\frac{99}{-100}\)
\(=\frac{-9}{100}\)
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cảm ơn bạn nhé ST kết bạn với mình nhé để mình có thể hỏi bài từ bạn, đi mình xin bạn đấy
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\(\frac{\left(1+\frac{2012}{1}\right)\left(1+\frac{2012}{2}\right).......\left(1+\frac{2012}{100}\right)}{\left(1+\frac{1000}{1}\right)\left(1+\frac{1000}{2}\right).....\left(1+\frac{1000}{2012}\right)}\)