Sum of a Series With Denominators of the form $(2^i) (3^j)(5^k)$ Can anyone solve this?
Find the sum of the series  $1 + \frac{1}{2} +\frac{1}{3} + \frac{1}{4} + \frac{1}{5}+ \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \cdots,$ where the denominators are of the form $(2^i) (3^j)(5^k)$?
The test came with the next answer choices:
a) $\frac{7}{2}$
b) $1$    
c) $3$   
d) $\frac{15}{4}$    
e) $\frac{3}{2}$
I thought this would tend to infinity. Maybe the test answer choices were wrong..

Consider $$(1 + \frac{1}{2} + \frac{1}{4} + \ldots + \frac{1}{2^n} + \ldots)(1 + \frac{1}{3} + \frac{1}{9} + \ldots + \frac{1}{3^n} + \ldots)(1 + \frac{1}{5} + \frac{1}{25} + \ldots + \frac{1}{5^n} + \ldots)$$
