Final answer:
The sum of the geometric series 400+200+100+... converges to 800 using the formula for the sum of an infinite geometric series, where the first term is 400 and the common ratio is 1/2.
Step-by-step explanation:
The series provided in the question is a geometric series whose first term is 400 and the common ratio is \(\frac{1}{2}\). The formula we use to evaluate the sum of an infinite geometric series is \(S = \frac{a}{1 - r}\), where \(S\) is the sum of the series, \(a\) is the first term, and \(r\) is the common ratio. In this case, we have \(a = 400\) and \(r = \frac{1}{2}\).
The sum of the series can be calculated as follows:
\[S = \frac{a}{1 - r} = \frac{400}{1 - \frac{1}{2}} = \frac{400}{\frac{1}{2}} = 400 \times 2 = 800\]
Therefore, the sum of the series \(400+200+100+\dots\) converges to 800, and the correct answer is C. 800.