The given infinite series can be rewritten as :
$ S = [1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{16} + ... ] + [ 1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + .... ] $
So now we just have to find the sum of two infinite series with common ratio r equals to $\frac{1}{2}$ and $\frac{1}{3}$ respectively.
Therefore, $ S = [ \frac{1}{(1- \frac{1}{2})} ] + [ \frac{1}{(1- \frac{1}{3})} ] = 2 + \frac{3}{2} = \frac{7}{2} $
Hence, Option B is the correct answer.
