Question

Tính tổng: S=3+\(\frac{3}{2}\)+\(\frac{3}{2^2}\)+...+\(\frac{3}{2^9}\)

Answer 1

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

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

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

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

Answer 2

\(2S=2\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)

\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)

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

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

tới đây thì bn tự tính nhé