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A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
B = \(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}=\frac{\left(2.3.4.5\right).\left(2.3.4.5\right)}{\left(1.2.3.4\right).\left(3.4.5.6\right)}=\frac{5.2}{1.6}=\frac{5}{3}\)
C = \(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{3}{2}.\frac{56}{305}=\frac{74}{305}\)
Bài làm:
1) \(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{50-49}{49.50}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(A=1-\frac{1}{50}=\frac{49}{50}\)
2) \(B=\frac{2^2.3^2.4^2.5^2}{1.2.3^2.4^2.5.6}=\frac{2.5}{6}=\frac{5}{3}\)
3) \(C=\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}\)
\(C=\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(C=\frac{3}{2}\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{61-59}{59.61}\right)\)
\(C=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(C=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(C=\frac{3}{2}.\frac{56}{305}=\frac{84}{305}\)
1.\(\frac{10+5}{4.5}=\frac{2.5+1.5}{4.5}=\frac{\left(2+1\right).5}{4.5}=\frac{3.5}{4.5}=\frac{3}{4}\)
2. \(\frac{2^2.9}{27.2}=\frac{2.2.3.3}{3.3.3.2}=\frac{2}{3}\)
\(=-2.\frac{2}{3}.\frac{1}{3}:\left(\frac{-1}{6}+0,5\right)-\left(-2009^0\right)-\left(-2\right)^2\)
\(=\frac{4}{3}.\frac{1}{3}:\left(\frac{-1}{6}+\frac{1}{2}\right)-1.4\)
\(=\frac{4}{3}.\frac{1}{3}+4\)
\(=4+4\)
\(=8\)
1. \(\frac{25}{100}x+x-\frac{1}{5}x=\frac{1}{5}\)
\(\Leftrightarrow\frac{1}{4}x+x-\frac{1}{5}x=\frac{1}{5}\)
\(\Leftrightarrow\left(\frac{1}{4}+1-\frac{1}{5}\right)x=\frac{1}{5}\)
\(\Leftrightarrow\frac{21}{20}x=\frac{1}{5}\)
\(\Leftrightarrow x=\frac{1}{5}:\frac{21}{20}\)
\(\Leftrightarrow x=\frac{4}{21}\)
1) \(\frac{2}{3}+x=-\frac{4}{5}\)
\(x=\left(-\frac{4}{5}\right)-\frac{2}{3}\)
\(x=-1\frac{7}{15}\)
Vậy \(x=-1\frac{7}{15}\)
2) \(\frac{2}{5}-x=-\frac{1}{3}\)
\(x=\frac{2}{5}-\left(-\frac{1}{3}\right)\)
\(x=\frac{11}{15}\)
Vậy \(x=\frac{11}{15}\)
3) \(1-\frac{x}{3}=1\frac{1}{2}\)
\(\frac{x}{3}=1-1\frac{1}{2}\)
\(\frac{x}{3}=-\frac{1}{2}\)
\(\Rightarrow x=\frac{\left(-1\right)\cdot3}{2}\)
\(x=-1\frac{1}{2}\)
4) \(1-\left(\frac{2x}{3}+2\right)=-1\)
\(\frac{2x}{3}+2=1-\left(-1\right)\)
\(\frac{2x}{3}+2=2\)
\(\frac{2x}{3}=2-2\)
\(\frac{2x}{3}=0\)
\(\Rightarrow x=0\)
Vậy \(x=0\)
1. Vì -5/7=70/x-3 =>-5.(x-3)=70.7
=>5x-15=490
=>5x=505
=>x=101
2. Vì 2.3^x-5=7
=>2.3^x=12
=>3^x=6
Sai đề rồi bạn ơi! ^.^
1. \(\Leftrightarrow\)-5*(x-3) = 70*7
\(\Leftrightarrow\)-5x + 15 = 490
\(\Leftrightarrow\)-5x = 435
\(\Leftrightarrow\)x = -87
2. 2*3x -5 =7
\(\Leftrightarrow\)2*3x = 12
\(\Leftrightarrow\)3x = 6
\(\Leftrightarrow\)x = 2
( Bài 2 em xem lại coi có sai đề không nha. Không có cái nào mà 3x = 6 hết, chỉ có 3x=6 thôi nha)
100.2.5.10 = 10.10.10.10 = 104
A = 103103 = 7.11.13.103
B = 102.102 = 22.32.17
C = 102.10.10102.10.10 = 22.3.17.103.5051
D = 104104 = 23.7.11.132