Đáp án:
Giải thích các bước giải:
`S=\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\frac{31}{32}+\frac{63}{64}+\frac{127}{128}`
`S=1-\frac{1}{2}+1-\frac{1}{4}+1-\frac{1}{8}+1-\frac{1}{16}+1-\frac{1}{32}+1-1-\frac{1}{64}+1-\frac{1}{128}-6`
`S=(1+1+1+1+1+1+1)-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128})-6`
`S=7-6-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128})`
`S=1-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128})`
Xét `\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}`
`=\frac{64+32+16+8+4+2+1}{128}`
`=\frac{127}{128}`
`⇒S=1-\frac{127}{128}=\frac{1}{128}`
