Consider the series $\displaystyle{ \sum_{n=1}^{\infty} \left( \frac{1}{n} - \frac{1}{n+1} \right) }$.

1. The series has the form $\displaystyle{ \sum_{n=1}^{\infty} a_n }$ where $a_n =$
2. The first five terms in the sequence $\lbrace a_n \rbrace$ are . Enter a comma separated list of numbers (in order).
3. The first five terms in the sequence of partial sums for this series are . Enter a comma separated list of numbers (in order).
4. The general formula for the partial sum $S_n$ is . Your answer should be in terms of $n$.
5. The sum of a series is defined as the limit of the sequence of partial sums, which means
   $\displaystyle{ \sum_{n=1}^{\infty} \left( \frac{1}{n} - \frac{1}{n+1} \right) = \lim_{n \to \infty} \bigg( }$ $\displaystyle{\bigg) = }$ .
6. Select all true statements (there may be more than one correct answer):
   A. Telescoping series always converge.
   B. The series converges to $0$.
   C. The series is a telescoping series (i.e., it is like a collapsible telescope).
   D. The sequence $\lbrace a_n \rbrace$ converges to $1$.
   E. The series converges to $1$.
   F. Most of the terms in each partial sum cancel out.
   G. The sequence $\lbrace a_n \rbrace$ converges to $0$.