
Alternating Series
A series with terms that alternate signs.

Alternating Series Test
An alternating series converges if the absolute values of its terms are decreasing and approach zero.

Comparison Test
A series with positive terms converges if there is another series with all terms greater or equal
which is known to converge. Similarly, a series with positive terms diverges if there is another
series with all terms lesser or equal which diverges.

Convergent
The property that the partial sums of a series have a welldefined limit.

Absolutely Convergent
The property that the sum of the absolute values of the terms in a series form a convergent series.
An absolutely convergent series is automatically convergent.

Divergent
A property of a series with partial sums that do not have a welldefined limit.

Geometric Series
A series characterized by a constant ratio between consecutive terms.

Integral Test
If f (x) is a positive decreasing function, the series f_{n} = f (n)
converges if and only if the integral
f (x)dx 

tends to a finite limit as n→∞.

Partial Sum
The sum of finitely many terms from the beginning of a series.

Power Series
A series of the form a_{n}x^{n} where a_{n} is a sequence of real numbers and
x is a variable.

Radius of Convergence
A power series a_{n}x^{n} converges absolutely either for all  x < r, or for
all real numbers x. We then say that the radius of convergence of the power series is r
or ∞, respectively.

Ratio Test
A method for determining convergence by computing the ratios between
consecutive terms of a series. Specifically, if there is a real
number 0≤C < 1 such that (a_{n+1}/a_{n})≤C for all
n > 0, then the series a_{n} converges. This is
nothing more than the comparison test applied to a geometric
series.

Series
A sum of the elements in a sequence.

Upper Bound
A number which is greater than or equal to all of the partial sums of a sequence.