Note that \(2^a2^b2^c....=2^{a+b+c...}\)
In your case \(a+b+c\) forms an infinite geometric series, ie. \(b = ar, c = ar^2, ...etc\)
The limit of the infinite geometric series here is \(\frac{a}{1-r}\) or \(\frac{1/3}{1-1/3}\)
You can complete the calculation.
