Question

Guess a formula for $a_e$. Use the subdivided unit square below to give a visual justification of your conjecture.

Answer 1

$a_1=\frac{1}{2},a_2=\frac{1}{2}+\frac{1}{4},a_3=\frac{1}{2}+\frac{1}{4}+\frac{1}{8},..........a_n=\frac{1}{2}+\frac{1}{4}+.......+\frac{1}{2^n}$
$a_1=1-\frac{1}{2},a_2=1-\frac{1}{4},a_3=1-\frac{1}{8}..............then{a}_n=?$