Nth Term Test for Divergence

Flashcards summarizing key terms and definitions related to the nth term test for divergence in calculus.

Nth Term Test for Divergence

A method to determine if a series diverges based on the limit of its nth term as n approaches infinity.

Converges

A series converges if the sum approaches a finite limit as n approaches infinity.

Diverges

A series diverges if the sum does not approach a finite limit as n approaches infinity.

Limit

The value that a function approaches as the input approaches some value, often considered as n approaches infinity in series.

Geometric Series

A series of the form a + ar + ar^2 + ar^3 + …, where a is the first term and r is the common ratio.

L'Hôpital's Rule

A method for finding limits of indeterminate forms by taking the derivatives of the numerator and denominator.

Absolute Value of R

In a geometric series, if the absolute value of the common ratio R is less than one, the series converges.

Horizontal Asymptotes

A horizontal line that a graph approaches as x approaches positive or negative infinity.

Conclusion Statement

The final statement that summarizes the result of the limit test, indicating whether the series converges or diverges.

Sum of Series

The total value obtained by adding all terms of a series together.