\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{20}}\)
\(2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^{19}}\)
\(\Rightarrow2A-A=1-\dfrac{1}{2^{20}}\)
\(\Rightarrow A=1-\dfrac{1}{2^{20}}\)
\(B=\dfrac{1}{4}+\dfrac{1}{4^2}+...+\dfrac{1}{4^{10}}\)
\(\Rightarrow4B=1+\dfrac{1}{4}+...+\dfrac{1}{4^9}\)
\(\Rightarrow4B-B=1-\dfrac{1}{4^{10}}=1-\dfrac{1}{\left(2^2\right)^{10}}=1-\dfrac{1}{2^{20}}\)
\(\Rightarrow3B=1-\dfrac{1}{2^{20}}\)
\(\Rightarrow A=3B\Rightarrow\dfrac{A}{B}=3\)
Đúng 0
Bình luận (0)
