Question

[Nguyễn Lan Hương]

Tính : \(\frac{1}{2}\)-\(\frac{1}{4}\)-\(\frac{1}{8}\)-\(\frac{1}{16}\)- ... - \(\frac{1}{1024}\)

Answer 1

[công chúa xinh xắn]

ta có : \(\frac{1}{2}=1-\frac{1}{2};\frac{1}{4}=\frac{1}{2}-\frac{1}{4};\frac{1}{8}=\frac{1}{4}-\frac{1}{8}\)

             \(\frac{1}{16}=\frac{1}{8}-\frac{1}{16};\frac{1}{1024}=\frac{1}{512}-\frac{1}{1024}\)

\(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-\frac{1}{16}-.....-\frac{1}{1024}\)

\(=1-\frac{1}{2}-\frac{1}{2}-\frac{1}{4}-\frac{1}{4}-\frac{1}{8}-\frac{1}{8}-\frac{1}{16}-\frac{1}{16}-....-\frac{1}{512}-\frac{1}{1024}\)

\(=1-\frac{1}{1024}\)

\(=\frac{1023}{1024}\)

Answer 2

[Nguyệt]

đặt D=-(1/2+1/4+1/8+....+1/1024)

D=-(1/2+1/2^2+....+1/2^10)

đặt A=1/2+...+1/2^10

2A = 1+1/2+...+1/2^9

2A-A=(1+1/2+...+1/2^9)-(1/2+...+1/2^10)

A=1-1/2^10

A=2^10-1/2^10

D=-2^10-1/2^10