Question

[Bảo Minh]

Ai giúp mình với

Answer 1

[Đoàn Đức Hà]

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

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

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

\(S=1-\frac{1}{2^{10}}=\frac{1023}{1024}\)