Cho \(a=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....+\frac{1}{512}\)
Nên \(2a=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)
\(2a-a=a=1-\frac{1}{512}=\frac{511}{512}\)
Vậy \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}=\frac{511}{512}\)
Bài này dễ.
Giải:
Đặt tổng trên là A, ta có:
\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{256}+\frac{1}{512}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{512}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\right)\)
\(A=1-\frac{1}{1024}\)
\(A=\frac{1023}{1024}\)
Chúc bạn học tốt.
