Tính:a)(1-1/4).(1-1/9).(1-1/16)....(1-1/225)
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tính :(1-1/4)(1-1/9)(1-1/16)(1-1/25)...... (1-1/196)(1-1/225)
A=3/4x8/9x15/16x...x224/225
A=3.8.15....224/4.9.16...225
A=(1.3)(2.4)(3.5)...(14.16)/2.2.3.3....15.15
A=(1.2.3...14)(3.4.5...16)/(2.3...15)(2.3...15)
A=16/15.2
A=8/15
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tính :(1-1/4)(1-1/9)(1-1/16)(1-1/25)...... (1-1/196)(1-1/225)
Tính:a)\(\left(\frac{1}{9}-1\right).\left(\frac{1}{10}-1\right)...\left(\frac{1}{2004}-1\right).\left(\frac{1}{2005}-1\right)\)
b)\(81^{10}-27^{13}-9^{21}⋮225\)
a,\(\left(\frac{1}{9}-1\right).\left(\frac{1}{10}-1\right)...\left(\frac{1}{2004}-1\right).\left(\frac{1}{2005}-1\right)\)
\(=\frac{-8}{9}.\frac{-9}{10}...\frac{-2003}{2004}.\frac{-2004}{2005}\)
\(=\frac{\left(-8\right).\left(-9\right)...\left(-2003\right).\left(-2004\right)}{9.10...2004.2005}\)
\(=\frac{-\left(8.9...2003.2004\right)}{9.10...2004.2005}\)
\(=\frac{-8}{2005}\)
b,Ta có: \(81^{10}-27^{13}-9^{21}\)
\(=\left(3^4\right)^{10}-\left(3^3\right)^{13}-\left(3^2\right)^{21}\)
\(=3^{40}-3^{39}-3^{42}\)
\(=3^{39}.3-3^{39}-3^{39}.3^3\)
\(=3^{39}.\left(3-1-3^3\right)\)
\(=3^2.3^{37}.\left(-25\right)\)
\(=3^{37}.\left(-225\right)⋮225\)
Vậy \(81^{10}-27^{13}-9^{21}⋮225\)
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Tính A
(1-1/4)*(1-1/9)*(1-1/16)*(1-1/25)*...*(1-1/196)*(1-1/225)
a)Tìm x : 2^2x-1 + 6.2^8 = 14.2^8
b) Tính : A = (1-1/4) . (1-1/9 ) . (1-1/16) . (1-1/25) ...........(1-1/196).(1-1/225)
\(a)\)
\(2^{2x-1}+6.2^8=14.2^8\)
\(\Leftrightarrow2^{2x-1}=14.2^8-6.2^8\)
\(\Leftrightarrow2^{2x-1}=8.2^8\)
\(\Leftrightarrow2^{2x-1}=2^3.2^8\)
\(\Leftrightarrow2x-1=11\)
\(\Leftrightarrow2x=11+1\)
\(\Leftrightarrow x=\frac{12}{2}\)
\(\Leftrightarrow x=6\)
\(b)\)
\(A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{25}\right)...\left(1-\frac{1}{196}\right)\left(1-\frac{1}{225}\right)\)
\(\Leftrightarrow A=\frac{3}{4}.\frac{8}{9}...\frac{224}{225}\)
\(\Leftrightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{14.16}{15.15}\)
\(\Leftrightarrow A=\frac{1.2.3.4...14.16}{2.2.3.3...25.25}\)
\(\Leftrightarrow A=\frac{1.2.3...14}{2.3.4...15}.\frac{3.4.5...16}{2.3.4...15}\)
\(\Leftrightarrow A=\frac{1}{15}.\frac{16}{2}\)
\(\Leftrightarrow A=\frac{8}{15}\)
a) Tìm x :2^2x-1 +6.2^8 = 142^8
b) Tính A = (1-1/4).(1-1/9).(1-1/16).(1-1/25)..........(1-1/196).(1-1/225)
SGK Cánh diều - Tập 2 - Trang 85
31 tháng 10 2023 lúc 23:33
Tính:a) dfrac{2}{3}+dfrac{4}{3} dfrac{9}{8}-dfrac{1}{8} dfrac{1}{6}+dfrac{2}{3} dfrac{3}{4}-dfrac{7}{16}b) 9+dfrac{2}{7} dfrac{3}{8}+10 7-dfrac{2}{11} dfrac{25}{4}-5c) dfrac{2}{3}timesdfrac{1}{4} dfrac{7}{11}timesdfrac{11}{2} dfrac{3}{7}:dfrac{4}{9} dfrac{9}{8}:dfrac{3}{4}d) 8timesdfrac{3}{7} ...
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Tính:
a) \(\dfrac{2}{3}+\dfrac{4}{3}\) \(\dfrac{9}{8}-\dfrac{1}{8}\) \(\dfrac{1}{6}+\dfrac{2}{3}\) \(\dfrac{3}{4}-\dfrac{7}{16}\)
b) \(9+\dfrac{2}{7}\) \(\dfrac{3}{8}+10\) \(7-\dfrac{2}{11}\) \(\dfrac{25}{4}-5\)
c) \(\dfrac{2}{3}\times\dfrac{1}{4}\) \(\dfrac{7}{11}\times\dfrac{11}{2}\) \(\dfrac{3}{7}:\dfrac{4}{9}\) \(\dfrac{9}{8}:\dfrac{3}{4}\)
d) \(8\times\dfrac{3}{7}\) \(\dfrac{3}{10}\times6\) \(6:\dfrac{5}{24}\) \(\dfrac{18}{7}:3\)
30 tháng 6 2021 lúc 16:04
* Tính:
a.\(\dfrac{-4}{3}.\sqrt{\left(-0,4\right)^2}\)
b.\(\sqrt[3]{\dfrac{3}{4}}.\sqrt[3]{\dfrac{9}{16}}\)
c.\(\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}\)
a) Ta có: \(\dfrac{-4}{3}\cdot\sqrt{\left(-0.4\right)^2}\)
\(=-\dfrac{4}{3}\cdot0.4\)
\(=\dfrac{-1.6}{3}=-\dfrac{8}{15}\)
b) Ta có: \(\sqrt[3]{\dfrac{3}{4}}\cdot\sqrt[3]{\dfrac{9}{16}}\)
\(=\sqrt[3]{\dfrac{27}{64}}=\dfrac{3}{4}\)
c) Ta có: \(\dfrac{1}{3+\sqrt{2}}+\dfrac{1}{3-\sqrt{2}}\)
\(=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{7}\)
\(=\dfrac{6}{7}\)
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Tính:
a) -5/7(14/5 - 7/10) : |-2/3| - 3/4(8/9 + 16/3) + 10/3(1/3 + 1/5)
b) 17/-26(1/6 - 5/3) : 17/13 - 20/3(2/5 - 1/4) + 2/3(6/5 - 9/2)
c) -8/9(9/8 - 3/2) + 5/4 : (5/2 - 15/4) - 3/4(10/9 - 8/3) : (-1/3)
d) 21/10 : (12/5 - 9/10) . (-4/7) - 3/2(1/6 - 7/12) + 1/5(3/2 - 1/4)
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
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