Question

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

 

Answer 1

2S=6+3+3/2+3/2²+...+3/2⁸

2S-S=(6+3+3/2+3/2²+...+3/2⁸) -(3+3/2+3/2²+...+3/2⁹)

S=6-3/2⁹=6-3/512=3069/512

Answer 2

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

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