Question

Tính tổng :

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

Answer 1

Ta có :

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

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

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

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

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

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