Consider the sequence $\displaystyle{ \lbrace a_n \rbrace = \left\lbrace \frac{1}{2^n} \right\rbrace }$.

1. The first five terms in this sequence are . Enter a comma separated list of numbers (in order).
2. The first five partial sums of this sequence are . Enter a comma separated list of numbers (in order).
3. The sum of the first $n$ terms of the sequence is the partial sum $S_n = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots + \frac{1}{2^n} =$ . Your answer should be in terms of $n$.
4. The sum of all terms in the sequence is defined as the the limit of the partial sums, which means
   $\displaystyle{ \sum_{n=1}^{\infty} \frac{1}{2^n} = \lim_{n \to \infty} \bigg( }$ $\displaystyle{\bigg) = }$ .
5. Select all true statements (there may be more than one correct answer):
   A. The sequence converges to $0$.
   B. The sequence converges to $1$.
   C. The limit of the sequence of partial sums is $0$.
   D. The limit of the sequence of partial sums is $1$.
   E. The series converges to $0$.
   F. The series converges to $1$.