Answer
True
Work Step by Step
$0.74999...=0.74+0.009+0.0009+0.00009+...$
$=0.74+\frac{9}{10^3}+\frac{9}{10^4}+\frac{9}{10^5}+...$
$=0.74+\frac{9}{10^3}(\frac{1}{10^0}+\frac{1}{10^1}+\frac{1}{10^2}+...)$
$=0.74+\frac{9}{10^3}\sum^{\infty}_{n=0}(\frac{1}{10})^n$
$=0.74+\frac{9}{10^3}\times\frac{1}{1-\frac{1}{10}}$
$=0.74+\frac{9}{10^3}\times\frac{10}{9}$
$=0.74+\frac{1}{100}$
$=0.74+0.01=0.75$
