\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{32}+\frac{1}{64}\)
=\(\frac{1}{1\cdot2}+\frac{1}{2\cdot2}+\frac{1}{2\cdot4}+\frac{1}{2\cdot16}+\frac{1}{2\cdot32}\)
=\(\frac{1}{2}\cdot\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{16}+\frac{1}{32}\right)\)
=\(\frac{1}{2}\cdot\frac{119}{64}\)
=\(\frac{119}{128}\)
Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
A * 2 = 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32
A * 2 - A = 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 - 1/2 - 1/4 - 1/8 - 1/16 - 1/32 - 1/64
A = 1/1 - 1/64
A = 63/64
\(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
= \(\left(\frac{1}{2}+\frac{1}{4}\right)+\left(\frac{1}{8}+\frac{1}{16}\right)+\left(\frac{1}{32}+\frac{1}{64}\right)\)
= \(\frac{3}{4}+\frac{3}{16}+\frac{3}{64}\)
= \(\left(\frac{3}{4}+\frac{3}{16}\right)+\frac{3}{64}\)
= \(\frac{15}{16}+\frac{3}{64}\)
= \(\frac{63}{64}\)
