\(S=3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\)
\(2S=2\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\right)\)
\(2S=6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\)
\(2S-S=\left(6+3+...+\dfrac{3}{2^8}\right)-\left(3+\dfrac{3}{2}+...+\dfrac{3}{2^9}\right)\)
\(S=6-\dfrac{3}{2^9}\)
Cái bài tính tổng đó hả?? Trên này mọi người đăng suốt ak!! mk làm hoài ko nhớ ở đâu nữa!
Ta có :
\(S=3+\dfrac{3}{2}+\dfrac{3}{2^2}+\dfrac{3}{2^3}+...................+\dfrac{3}{2^9}\)
\(\Rightarrow2S=2\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+\dfrac{3}{2^3}+.................+\dfrac{3}{2^9}\right)\)
\(\Rightarrow2S=6+3+\dfrac{3}{2}+\dfrac{3}{2^2}+\dfrac{3}{2^3}+...............+\dfrac{3}{2^8}\)
\(\Rightarrow2S-S=\left(6+3+\dfrac{3}{2}+\dfrac{3}{2^2}+......+\dfrac{3}{2^8}\right)-\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+........+\dfrac{3}{2^9}\right)\)
\(\Rightarrow S=6-\dfrac{3}{2^9}\)
\(\Rightarrow S=6-\dfrac{3}{512}\)
\(\Rightarrow S=\dfrac{3069}{512}\)
\(S=3+\dfrac{3}{2^2}+\dfrac{3}{2^3}+...+\dfrac{3}{2^9}\)
\(2S=6+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^8}\)
\(\Rightarrow2S-S=6-\dfrac{3}{2^9}\)
\(\Rightarrow S=6-\dfrac{3}{2^9}\)
\(\Rightarrow S=6-\dfrac{3}{512}\)
\(\Rightarrow S=\dfrac{9216}{1536}-\dfrac{9}{1536}\)
\(\Rightarrow S=\dfrac{3069}{512}\)
Vậy \(S=\dfrac{3069}{512}\).
