Question

Tính nhanh : F = \(\frac{1}{2}\)+  \(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+.....+\frac{1}{4096}\)

Answer 1

F=đã cho

=>1/2F=1/4+1/8+1/16+...+1/8192

=>F-1/2F=1/2-1/8192

=>1/2F=1/2-1/8192

=>F=1-1/4096

=>F=4095/4096

Vậy......

Answer 2

Ta có : \(F=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......+\frac{1}{4096}\)

\(\Rightarrow2F=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+.....+\frac{1}{2048}\)

\(\Rightarrow2F-F=1-\frac{1}{4096}\)

\(\Rightarrow F=\frac{4095}{4096}\)