\(y=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(\frac{1}{2}y=\frac{1}{2}\times\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(\frac{1}{2}y=\frac{1}{2}\times1+\frac{1}{2}\times\frac{1}{2}+...+\frac{1}{2}\times\frac{1}{32}\)
\(\frac{1}{2}y=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(y-\frac{1}{2}y=\left(1+\frac{1}{2}+\frac{1}{4}+...+\frac{1}{32}\right)-\left(\frac{1}{2}+\frac{1}{4}+..+\frac{1}{64}\right)\)
\(\left(1-\frac{1}{2}\right)y=1-\frac{1}{64}\)
\(\frac{1}{2}y=\frac{63}{64}\)
\(y=\frac{63}{64}\div\frac{1}{2}=\frac{63}{32}\)
