Infinite Sequences and Series (BC Only)

Which value can serve as the common ratio ($r$) in a convergent geometric series?

What must be true about the absolute value of the common ratio ($r$) in a geometric series for it to converge?

If the second term of a geometric series is $12$ and the common ratio is $\frac{1}{2}$, what is the sum of the first four terms?

An infectious disease spreads such that each person infected transmits it to three more people every week; if patient zero starts off an outbreak, how many total infections will occur within five weeks?

If the sum of an infinite geometric series is 0, what can be said about the common ratio?

Given a geometric series with a common ratio of $-3$, which expression represents the sum from $n=4$ to $n=7$ if the third term is $27$?

Considering that traditional methods focus on algebraic manipulation, what is an effective alternative calculus-based technique for determining if the geometric series $\sum \left( -\frac{2}{5} \right)^n$ converges and finding its sum?

What is the sum of the geometric series $3 + \frac{9}{2} + \frac{27}{4} + ...$ to infinity?

If the common ratio of a geometric series is -1, what can be said about the series?

Infinite series described by $\sum_{n=1}^{\infty} f(n) = g(n) + h(n)$, with $g(.)$ and $h(.)$ being geometric series with ratios $r$ and $s$ respectively. If the sum of $g$ is calculable as fifteen and the sum of $h$ is infinity, what is the overall summation $f$?