The following GMAT Problem Solving question tests your understanding of how to find the sum of an arithmetico-geometric series. This is a difficult question and you should expect something along these lines if you are scoring Q49+ on the GMAT quantitative section.
The limiting sum of the infinite series
$$ \dfrac{1}{2} + \dfrac{3}{4} + \dfrac{5}{8} + \dfrac{7}{16} + \dfrac{9}{32} + \ldots $$
whose $n$-th term is $\dfrac{2n-1}{2^n}$ is:
- $\quad \dfrac{5}{2}$
- $\quad 3$
- $\quad \dfrac{7}{2}$
- $\quad \dfrac{15}{4}$
- $\quad 4$