\(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(y=\frac{1}{2}\times\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)\)
\(y=\frac{1}{2}\times\frac{31}{16}\)
\(y=\frac{31}{32}\)
y=1/2x[1+1/2+1/4+1/8+1/16]
=1/2x31/16
=31/32
\(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(y=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\right)+\left(\frac{1}{16}+\frac{1}{32}\right)\)
\(y=\left(\frac{4}{8}+\frac{2}{8}+\frac{1}{8}\right)+\left(\frac{2}{32}+\frac{1}{32}\right)\)
\(y=\frac{7}{8}+\frac{3}{32}\)
\(y=\frac{28}{32}+\frac{3}{32}=\frac{31}{32}\)
\(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)
\(2y=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\times2\)
\(2y=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+\frac{1}{16}\times2+\frac{1}{32}\times2\)
\(2y=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2y-y=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\right)\)
\(y=1-\frac{1}{32}\)
\(y=\frac{31}{32}\)
\(y=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16} +\frac{1}{32}\)
\(=\frac{1}{2}.\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)\)
\(=\frac{1}{2}.\frac{31}{16}\)
\(=\frac{31}{32}\)