Question

Tính tổng:

S= 3 + 3/2 + 3/2 bình phương +....+ 3/ 2 mũ 9

Answer 1

S=3+3/2+3/3^2+3/2^3+3/2^4+...........+3/2^9

2S=6+3/2+3/2^2+3/2^3+..........+3/2^8

S=2S-S=(6+3+3/2+3/2^2+3/2^3+3/2^4+...........+3/2^8)-(3+3/2+3/2^2+3/2^3+3/2^4+.....+3/2^9)

S=6-3/2^9

S=3069/512.

Answer 2

\(S=3\cdot\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)=3\cdot\left(1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{2^2}+...+\frac{1}{2^8}-\frac{1}{2^9}\right)\)                                               \(=3\cdot\left(1+1-\frac{1}{2^9}\right)=3\left(2-\frac{1}{2^9}\right)=3\cdot\frac{1023}{512}=\frac{3069}{512}\)