Answer
$a_1$=$1$
$a_2$=$\frac{3}{2}$
$a_3$=$\frac{7}{4}$
$a_4$=$\frac{15}{8}$
$a_5$=$\frac{31}{16}$
$a_6$=$\frac{63}{32}$
$a_7$=$\frac{127}{64}$
$a_8$=$\frac{255}{128}$
$a_9$=$\frac{511}{256}$
$a_{10}$=$\frac{1023}{512}$
Work Step by Step
$a_1$=$1$
$a_2$=$1+\frac{1}{2}$=$\frac{3}{2}$
$a_3$=$\frac{3}{2}+\frac{1}{(2)^2}$=$\frac{7}{4}$
$a_4$=$\frac{7}{4}+\frac{1}{(2)^3}$=$\frac{15}{8}$
$a_5$=$\frac{15}{8}+\frac{1}{(2)^4}$=$\frac{31}{16}$
$a_6$=$\frac{63}{32}$
$a_7$=$\frac{127}{64}$
$a_8$=$\frac{255}{128}$
$a_9$=$\frac{511}{256}$
$a_{10}$=$\frac{1023}{512}$
