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Write the series using sigma notation:

$\displaystyle{ 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \cdots = \sum_{n=0}^{\infty} }$

The sum of a series is defined as the limit of the sequence of partial sums, $\lbrace S_n \rbrace$ , which means

$\displaystyle{ 1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \cdots = \lim_{n \to \infty} \bigg( }$ $\displaystyle{\bigg) = }$ .

Select all true statements (there may be more than one correct answer):
A. The series is a geometric series.
B. The series is a telescoping series (i.e., it is like a collapsible telescope).
C. The series is an alternating series.
D. The series converges.
E. The series is a p-series.