Question

Rút gọn tổng sau:

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}}\)

Answer 1

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

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

=> 2S - S = ( \(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)  ) - ( \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\))

S = 1 - \(\frac{1}{2^{10}}\)

Answer 2

\(S=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{10}}\)

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

=> \(S=1-\frac{1}{2^{10}}\)

Study well ! >_<

Answer 3

S=1/2+1/2²+1/2³+.....+1/2¹⁰

\(\Rightarrow\)2S = 1+1/2+....+1/2⁹

\(\Rightarrow\)2S-S=1-1/2¹⁰

\(\Rightarrow\)S=1023/1024