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a) \(A=\frac{6^3.9^7.4^3-16^2.81^4}{\left(24.3\right)^2}\)
\(A=\frac{2^3.3^3.3^{14}.2^6-2^8.3^{16}}{24^2.3^2}\)
\(A=\frac{2^9.3^{17}-2^8.3^{16}}{3^2.8^2.3^2}\)
\(A=\frac{2^8.3^{16}.\left(2.3-1\right)}{3^4.2^6}\)
\(A=\frac{2^8.3^{16}.5}{3^4.2^6}=2.3^{12}.5=10.3^{12}\)
b) \(B=2198+123-198-1123+42\)
\(B=\left(2198-198\right)+\left(123-1123\right)+42\)
\(B=2000-1000+42=1042\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\text{ }\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right).0\)
\(Q=0\)
Q=(1/99+12/999+123/999).(1/2-1/3-1/6) =(1/99+12/999+123/999).0 Q=0
\(\left(\frac{1}{3}+\frac{3}{4}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=\left(\frac{4}{12}+\frac{9}{12}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=\left(\frac{4+9-13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0:\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0\)
Study well ! >_<
(13 +34 - 1312 ) : (1213 + 123234 +12342345 )
=\(\left(\frac{4}{12}+\frac{9}{12}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
= \(\left(\frac{4+9-13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
= \(0:\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0\)
Xin lỗi, mình chỉ làm được câu 1 thôi
\(A=\frac{1}{7}\left(\frac{555}{222}+\frac{4444}{12221}+\frac{33333}{244442}+\frac{11}{330}+\frac{13}{60}\right)\)
\(A=\frac{1}{7}\left(\frac{5.111}{2.111}+\frac{4.1111}{11.1111}+\frac{3.11111}{22.11111}+\frac{11}{11.30}+\frac{13}{60}\right)\)
\(A=\frac{1}{7}\left(\frac{5}{2}+\frac{4}{11}+\frac{3}{22}+\frac{1}{30}+\frac{13}{60}\right)\)
\(A=\frac{1}{7}\left[\left(\frac{5}{2 }+\frac{1}{30}+\frac{13}{60}\right)+\left(\frac{4}{11}+\frac{3}{22}\right)\right]\)
\(A=\frac{1}{7}\left[\left(\frac{150}{60}+\frac{2}{60}+\frac{13}{60}\right)+\left(\frac{8}{22}+\frac{3}{22}\right)\right]\)
\(A=\frac{1}{7}\left(\frac{11}{4}+\frac{1}{2}\right)\)
\(A=\frac{1}{7}.\frac{13}{4}\)
\(A=\frac{13}{21}\)
c)\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2012}}\)
\(2A=2\left(1+\frac{1}{2}+\frac{1}{2^2}+.....+\frac{1}{2^{2012}}\right)\)
\(2A=2+1+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2011}}\)
\(2A-A=\left(2+1+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....\frac{1}{2^{2012}}\right)\)
\(A=2-\frac{1}{2^{2012}}\)
1/
A=1/1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100
A=1/1-1/100
Vì 1/100>0
-->1/1-1/100<1
-->A<1
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Dành riêng luôn
\(-\frac{1123}{123}+123-\frac{1234}{3456}\)
\(=\frac{14006}{123}-\frac{1234}{3456}\)
\(=113,5128585\)