1 + \dfrac{1}{2} +\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{32} +\dfrac{1}{64} + \dfrac{1}{128}
Bạn thiếu phân số [TEX]\frac{1}{16}[/TEX] nhé!
Gọi tổng trên là A, ta có:
[TEX]A=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+\dfrac{1}{32} +\dfrac{1}{64} + \dfrac{1}{128}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{32} +\dfrac{1}{64} + \dfrac{1}{128}+\frac{1}{128}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{32} +\dfrac{1}{64} + \dfrac{2}{128}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{32} +\dfrac{1}{64} + \dfrac{1}{64}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{32} +\dfrac{2}{64}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{32} +\dfrac{1}{32}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{2}{32}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{16}+ \dfrac{1}{16}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{2}{16}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{8} + \frac{1}{8}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{2}{8}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{4} + \dfrac{1}{4}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{2}{4}[/TEX]
[TEX]A+\frac{1}{128}=1+\frac{1}{2}+\dfrac{1}{2}[/TEX]
[TEX]A+\frac{1}{128}=1+1[/TEX]
[TEX]A=2-\frac{1}{128}[/TEX]
[TEX]A=1\frac{127}{128}[/TEX]