Answer:
The series -1+2+(-4)+8+... is an arithmetic series because it has a common difference between consecutive terms. Specifically, the common difference is -4 - 2 = -6.
To determine whether the series is convergent or divergent, we need to find its sum. The sum of an arithmetic series is given by the formula:
sum = (n/2)(a1 + an)
where n is the number of terms in the series, a1 is the first term, and an is the nth term.
Since the series is infinite, we cannot determine its sum using this formula. However, we can determine its sum by taking the limit as n approaches infinity. Using the formula above, we find that the sum is equal to:
sum = (infinity/2)(-1 + infinity)
Since the series contains an infinite number of negative terms, it is divergent.