I came across the following problem that says:
The set of limit points of the sequence $1,\dfrac12,\dfrac14,\dfrac34,\dfrac18,\dfrac38,\dfrac58,\dfrac78,\dfrac1{16},\dfrac3{16},\dfrac5{16},\dfrac7{16},\dfrac9{16},\ldots$ is which of the following?
(a) $[0,1]$
(b) $(0,1]$
(c) the set of all rational numbers in $[0,1]$
(d) the set of all rational numbers in $[0,1]$ and of the form $m/2^n$ where $m$ and $n$
are integers.
Please help. Thanks in advance for your time.