Question

Tính tổng:

S=\(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^9}\)

Giúp mình nha

Answer 1

S=..... (đề bài)

\(\Rightarrow2S=2\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)

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

\(\Rightarrow2S-S=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)

\(\Rightarrow S=1-\frac{1}{2^9}=1-\frac{1}{256}=\frac{255}{256}\)