Question

tính nhanh 

1/2+1/4+1/8+1/16...+512=?

viết cả cách giả ^_^

Answer 1

đặt tên là A

ta có :

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+..\frac{1}{512}\)

\(2A=2.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\right)\)

\(2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\)

\(2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{256}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...+\frac{1}{512}\right)\)

\(A=1-\frac{1}{512}\)

\(A=\frac{511}{512}\)

Answer 2

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