Conditionally Convergent

Definition

A series ∑a_n is conditionally convergent if the series converges, but the absolute value of the terms, ∑|a_n|, diverges. In other words, the series converges when both positive and negative terms are summed together.

Related terms

Absolute Convergence: When a series ∑a_n converges and so does ∑|a_n|. In this case, all terms in the series have the same sign.

Divergence Test: A test used to determine if a series diverges by checking if its limit as n approaches infinity is not zero.

Harmonic Series:

The infinite sum of reciprocals of positive integers 1 + 1/2 + 1/3 + ... which is known to diverge.