Question

1/2+1/4+1/8+1/16+......+/256+1/512

 

Answer 1

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 \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}=\frac{511}{512}\)

Answer 2

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.