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\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)
= \(\frac{1x1x1}{1x2x4}x\frac{2.2.1}{1.1.2.2}=\frac{1}{8}.1=\frac{1}{8}\)
=1X2X3/1X2X3X4X2= 1/8 =3X2X2X2X5/3X2X2X5X2= 1/1
=1/8X1/1=1/8
\(\frac{1.2.6.4.6.4.5.2}{2.3.6.8.6.2.2.2.8.10}=\frac{1}{96}\)
\(=\frac{1}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+...+\frac{2}{12\times14}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{12}-\frac{1}{14}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{14}\right)=\frac{1}{2}\times\frac{3}{7}=\frac{3}{14}\)
\(A=\frac{1}{2\times4}+\frac{1}{4\times6}+\frac{1}{6\times8}+...+\frac{1}{2012\times2014}\)
\(=\frac{1}{2}\times(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2012\times2014})\)
\(=\frac{1}{2}\times(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2012}-\frac{1}{2014})\)
\(=\frac{1}{2}\times(\frac{1}{2}-\frac{1}{2014})\)
\(=\frac{1}{2}\times(\frac{1007}{2014}-\frac{1}{2014})\)
\(=\frac{1}{2}\times\frac{503}{1007}\)
\(=\frac{503}{2014}\)
Ta có ; \(\frac{1}{2}=\frac{1007}{2014}\)
Vậy A bé hơn B
Chúc bạn học tốt
\(\frac{5^2\times6^{11}\times16^2+6^2\times12^6\times15^2}{2\times6^{12}\times10^4-81^2\times960^3}\)
\(=\frac{5^2\times\left(2\times3\right)^{11}\times\left(2^4\right)^2+\left(2\times3\right)^2\times\left(2^2\times3\right)^6\times\left(3\times5\right)^2}{2\times\left(2\times3\right)^{12}\times\left(2\times5\right)^4-\left(3^4\right)^2\times\left(2^6\times3\times5\right)^3}\)
\(=\frac{5^2\times2^{19}\times3^{11}+2^{14}\times3^{10}\times5^3}{2^{17}\times5^4\times3^{12}-3^{11}\times2^{18}\times5^3}\)
\(=\frac{5^2\times3^{10}\times2^{14}\times\left(2^5\times3+5\right)}{2^{17}\times5^3\times3^{11}\times\left(5\times3-2\right)}\)
\(=\frac{2^5\times3+5}{2^3\times5\times3\times12}\)
\(=\frac{32\times3+5}{8\times15\times12}=\frac{96+5}{120\times12}=\frac{101}{1440}\)
A) \(\frac{1}{6}\) = 0,1666666665
B) 0,1666669167
\(\frac{1}{6}\) < \(\frac{111111}{666665}\)
Bạn lấy tử chia cho mẫu là ra