A mathematician is reviewing fundamental vocabulary related to infinite series
MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A mathematician is reviewing fundamental vocabulary related to infinite series.
(a) State the definitions of “absolute convergence” and “conditional convergence” for an infinite series ∑n=1∞an.
(b) Consider the series n=1∑∞n2(−1)n+1. Indicate whether this series is absolutely convergent, conditionally convergent, or divergent, and provide a brief justification.
(c) Give the precise statement that relates the convergence behavior of a rearranged series to the type of convergence (absolute or conditional) of the original series. In one or two sentences, distinguish how this property differs for absolutely versus conditionally convergent series.