Answer
$14/33$
Work Step by Step
$S_∞ = .4242424242424242$
$.4242424242424242424242 = 42/100 + 42/10000 + 42/1000000 + 42/100000000 + . . . $
The first terms is $42/100$ and the common ratio is $1/100$
$S_∞ = a_1/(1-r)$
$S_∞ = 42/100 /(1-1/100)$
$S_∞ = 42/100 / 99/100$
$S_∞ = 42/99$
$42/99 = 14*3/33*3$
$42/99 = 14/33$
