Question

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

Answer 1

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

\(\Rightarrow A=3.\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)\)

Đặt \(S=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

\(\Rightarrow2S=2+1+\frac{1}{2}+...+\frac{1}{2^8}\)

\(\Rightarrow2S-S=\left(2+1+\frac{1}{2}+...+\frac{1}{2^8}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^9}\right)\)

\(\Rightarrow S=2-\frac{1}{2^9}\)

Mà \(A=3.S\)

\(\Rightarrow A=3.\left(2-\frac{1}{2^9}\right)\)

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

Chúc bạn học tốt !!!