C = \(\frac{3}{2}\)+ \(\frac{3}{4}\)+\(\frac{3}{8}\)+ ..... + \(\frac{3}{64}\)
(Giải chi tiết)
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a) \(8466.15+170.4233=4233.2.15+170.4233=4233.30+170.4233=4233.\left(30+170\right)=4233.200=846600\)
b) \(1122.34+2244.83=1122.34+1122.2.83=1122.34+1122.166=1122.\left(34+166\right)=1122.200=224400\)
Bài 1 :
\(a)3^5\cdot4^5=12^5\)
Bài 2 :
\(a)\)Ta có : \((2x+1)^3=27\)
\(\Rightarrow(x+1)^3=3^3\)
\(\Rightarrow2x-1=3\)
\(\Rightarrow x=3+1\)
\(\Rightarrow x=4\)
\(\Rightarrow x=\frac{4}{2}\Rightarrow x=2\)
Còn câu b tự làm nhé
\(3^5.4^5=\left(3.4\right)^5=12^5=248832\)
\(\left(2x+1\right)^3=27\)
<=> \(\left(2x+1\right)^3=3^3\)
<=> \(2x+1=3\)
<=> \(x=1\)
\(\frac{2}{3}\cdot x-\frac{3}{2}\cdot x=\frac{5}{12}\)
\(\Rightarrow\frac{2}{3}-\frac{3}{2}\cdot x=\frac{5}{12}\)
\(\Rightarrow\frac{-5}{6}\cdot x=\frac{5}{12}\)
\(\Rightarrow x=\frac{5}{12}:\frac{-5}{6}=\frac{5}{12}\cdot\frac{6}{-5}=\frac{1}{-2}\)
\(\Rightarrow x=\frac{1}{-2}\)
Chúc bạn học tốt
\(C=\frac{3}{2}+\frac{3}{4}+.....+\frac{3}{64}\)
\(=3\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{64}\right)\)
\(=3\left(\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^6}\right)\)
Đặt : \(H=\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^6}\)
\(\Leftrightarrow2H=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^5}\)
\(\Leftrightarrow2H-H=\left(1+\frac{1}{2}+....+\frac{1}{2^5}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^6}\right)\)
\(\Leftrightarrow H=1-\frac{1}{2^6}\)
\(\Leftrightarrow C=3\left(1-\frac{1}{2^6}\right)=3-\frac{3}{2^6}\)
\(C=\frac{3}{2}+\frac{3}{4}+\frac{3}{8}+...+\frac{3}{64}\)
\(C=3.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{64}\right)\)
\(C=3.\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\right)\)(1)
Đặt \(D=\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\)
\(\Rightarrow2D=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^5}\)
\(\Rightarrow2D-D=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^5}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^6}\right)\)
\(D=1-\frac{1}{2^6}\)
Thay D vào (1) ta có:
\(C=3.\left(1-\frac{1}{2^6}\right)\)
\(C=3.\left(1-\frac{1}{64}\right)\)
\(C=3.\frac{63}{64}\)
\(C=\frac{189}{64}\)
Tham khảo nhé