Question

S = 3 + 3/2 + 3/2^2 +...+3/2^9

Answer 1

Ta có:

\(S=3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\)

\(\Rightarrow S=3\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\)

\(\Rightarrow2S=3\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)\)

\(\Rightarrow2S-S=3\left[\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)\right]\)

\(\Rightarrow S=3\left(2-\dfrac{1}{2^9}\right)\)

\(\Rightarrow S=3.\dfrac{1023}{512}=\dfrac{3069}{512}\)

Vậy \(S=\dfrac{3069}{512}\)