General form of a geometric series (starting from n=0)?
$$\sum_{n=0}^{\infty} a cdot r^n$$
General form of a geometric series (starting from n=1)?
$$\sum_{n=1}^{\infty} a cdot r^{n-1}$$
Formula for the sum of a converging geometric series?
$$\sum_{n=1}^{\infty} acdot r^{n-1} = \sum_{n=0}^{\infty} a cdot r^n = \frac{a}{1-r}$$
What does the Geometric Series Test state?
A geometric series converges if 0 < |r| < 1 and diverges if |r| ≥ 1, where 'r' is the common ratio.
What is a geometric series?
A series with a constant ratio between successive terms.
What is 'a' in a geometric series?
'a' is the initial term of the geometric series.
What is 'r' in a geometric series?
'r' is the common ratio between consecutive terms in a geometric series.
What does it mean for a series to converge?
A series converges if its partial sums approach a finite limit.
What does it mean for a series to diverge?
A series diverges if its partial sums do not approach a finite limit.
