\(\frac{10\cdot10\cdot10\cdot....\cdot10}{250sohang}\) = ?
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\(A=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}...\frac{9^2}{9.10}=\frac{1^2.2^2.3^2...9^2}{1.2.2.3.3.4.4...9.10}=\frac{1.2^2.3^2...9^2}{1.2^2.3^2.4^2...10^2}=\frac{1}{10^2}=\frac{1}{100}\)
\(0,8\cdot2\frac{2}{3}\cdot10\cdot0,375\cdot\left(\frac{-5}{8}\right)\)
\(=\frac{4}{5}\cdot\frac{8}{3}\cdot10\cdot\frac{3}{8}\cdot\left(\frac{-5}{8}\right)\)
\(=\left(\frac{8}{3}\cdot\frac{3}{8}\right)\cdot\left(\frac{4}{5}\cdot10\right)\cdot\left(\frac{-5}{8}\right)\)
\(=1\cdot8\cdot\left(\frac{-5}{8}\right)\)
\(=8\cdot\left(\frac{-5}{8}\right)\)
\(=-5\)
~Học tốt~
\(\frac{2.6.10+6.10.14+10.14.18+...+194.198.202}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3.1.3.5+2^3.3.5.7+2^3.97.99.101}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3\left(1.3.5+3.5.7+...+97.99.101\right)}{1.3.5+3.5.7+...+97.99.101}\)
\(=\frac{2^3}{1}=8\)
Vậy A = 8
\(\frac{6^2}{5\cdot7}\cdot\frac{7^2}{6\cdot8}\cdot\frac{8^2}{7\cdot9}\cdot\frac{9^2}{8\cdot10}\)
=\(\frac{6\cdot6}{5\cdot7}\cdot\frac{7\cdot7}{6\cdot8}\cdot\frac{8\cdot8}{7\cdot9}\cdot\frac{9\cdot9}{8\cdot10}\)
=\(\frac{6\cdot7\cdot8\cdot9}{5\cdot6\cdot7\cdot8}\cdot\frac{6\cdot7\cdot8\cdot9}{7\cdot8\cdot9\cdot10}\)
=\(\frac{9}{5}\cdot\frac{3}{5}\)=\(\frac{27}{25}\)
**** MIK
\(=\frac{6.6}{5.7}.\frac{7.7}{6.8}.\frac{8.8}{7.9}.\frac{9.9}{8.10}\)
\(=\frac{6.6.7.7.8.8.9.9}{5.6.7.8.9.10.8.7}\)
\(=\frac{27}{25}\)
\(\frac{\frac{75}{100}:\frac{5}{2}+\left(\frac{3}{4}\right)^2-\frac{3}{4}:\frac{149}{4}}{\left(\frac{-121}{200}-\frac{83}{200}\right):\left(\frac{-1}{100}\right)}=\frac{\frac{3}{10}+\frac{9}{16}-\frac{3}{149}}{\frac{-51}{50}:\frac{-1}{100}}=\frac{\frac{69}{80}-\frac{3}{149}}{102}=0,008258487595\)
\(\left(\sqrt{\frac{1}{4}\cdot\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\cdot10\sqrt{2}\right):\frac{1}{8}\)
\(=\left(\sqrt{\frac{1}{4}\cdot\frac{1\cdot2}{2\cdot2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\cdot10\sqrt{2}\right):\frac{1}{8}\)
\(=\left(\sqrt{\frac{1}{4}\cdot\frac{2}{4}}-\frac{3}{2}\sqrt{2}+8\sqrt{2}\right):\frac{1}{8}\)
\(=\left(\sqrt{\frac{2}{16}}-\frac{3}{2}\sqrt{2}+8\sqrt{2}\right):\frac{1}{8}\)
\(=\left(\frac{1}{4}\sqrt{2}-\frac{3}{2}\sqrt{2}+8\sqrt{2}\right):\frac{1}{8}\)
\(=\sqrt{2}\left(\frac{1}{4}-\frac{3}{2}+8\right):\frac{1}{8}\)
\(=\sqrt{2}\left(\frac{1}{4}-\frac{6}{4}+\frac{32}{4}\right):\frac{1}{8}\)
\(=\sqrt{2}\cdot\frac{27}{4}:\frac{1}{8}\)
\(=\frac{27\sqrt{2}}{4}\cdot\frac{8}{1}\)
\(=2\cdot27\sqrt{2}=54\sqrt{2}\)
\(\Rightarrow\left(\sqrt{\frac{1}{4}\cdot\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\cdot10\sqrt{2}\right):\frac{1}{8}=54\sqrt{2}\)
\(\left(\frac{1}{4}\sqrt{2}-\frac{3}{2}\sqrt{2}+\frac{4}{5}.10\sqrt{2}\right):\frac{1}{8}\)
=\(\sqrt{2}\)(1/4-3/2+8):1/8
=\(\sqrt{2}\).27/4.8
=54\(\sqrt{2}\)
10 * 10 * 10 ... * 10 có tất cả 25 số hạng
suy ra có tất cả 25 số 0
vậy tích của nó là 10000....000 gồm 25 số hạng
10000000...00000
25 so 0