\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(=\frac{1x64}{2x64}+\frac{1x32}{4x32}+\frac{1x16}{8x16}+\frac{1x8}{16x8}+\frac{1x4}{32x4}+\frac{1x2}{64x2}+\frac{1}{128}\)
\(=\frac{64}{128}+\frac{32}{128}+\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}\)
\(=\left(\frac{64}{128}+\frac{1}{128}\right)+\left(\frac{32}{128}+\frac{8}{128}\right)+\left(\frac{16}{128}+\frac{4}{128}\right)\)
\(=\frac{65}{128}+\frac{40}{128}+\frac{20}{128}\)
\(=125\)
nhầm , phải bằng\(\frac{125}{128}\)mới đúng
(cách làm ở dưới)
1/2 = 1 - 1/2
1/4 = 1/2 - 1/4
1/8 = 1/4 - 1/8
1/16 = 1/8 - 1/16
1/32 = 1/16 - 1/32
1/64 = 1/32 - 1/64
1/128 = 1/64 - 1/128
=> 1 - 1.2 + 1/2 -1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64+ 1/64 - 1/128
=> 1 - 1/128 = 127/128