Find the 7th term of the geometric series 1 + (2)/(sqrt(3)) + (4)/(3) + (8)/(3sqrt(3)) + and determine if its sum to infinity exists.

The given series is $1 + \frac{2}{\sqrt{3}} + \frac{4}{3} + \frac{8}{3\sqrt{3}} + \dots$.
This is a geometric series.
The first term is $a = 1$.
The common ratio $r$ is found by dividing the second term by the first term:

The formula for the $n$-th term of a geometric series is $T_n = a \cdot r^{n-1}$.
For the 7th term, $n=7$:

The 7th term is $\frac{64}{27}$.

The calculated 7th term is $\frac{64}{27}$, which corresponds to option (C).
The answer for question 5 is $\boxed{\text{C}}$.

For a geometric series to have a sum to infinity, the absolute value of the common ratio $|r|$ must be less than 1.
The common ratio is $r = \frac{2}{\sqrt{3}}$.
To check if $|r| < 1$:

Since $r \approx 1.1547 > 1$, the condition $|r| < 1$ is not met. Therefore, the sum to infinity of this series does not exist.

The conclusion is that the sum to infinity does not exist, which corresponds to option (D).
The answer for question 6 is $\boxed{\text{D}}$.