Question

tính:

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

Answer 1

Ta có:

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

\(\Rightarrow2S=2\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\right)\)

\(\Rightarrow2S=6+3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^8}\)

\(\Rightarrow2S-S=\left(6+3+\dfrac{3}{2}+...+\dfrac{3}{2^8}\right)-\left(3+\dfrac{3}{2}+\dfrac{3}{2^2}+...+\dfrac{3}{2^9}\right)\)

\(\Rightarrow S=6-\dfrac{3}{2^9}=6-\dfrac{3}{512}=\dfrac{3069}{512}\)

Vậy \(S=\dfrac{3069}{512}\)