Infinite series can be classified according to the manner in which their terms…
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Infinite series can be classified according to the manner in which their terms approach zero.
Part (a) Describe what it means for the series n=1∑∞an to converge absolutely.
Part (b) Describe what it means for the same series to converge conditionally.
Part (c) Provide one explicit example of a series that is conditionally convergent but not absolutely convergent. State the general term of your series and give a full justification for both its convergence and the failure of its absolute convergence.
Part (d) Explain whether rearranging the terms of an absolutely convergent series can change its numerical sum. Support your answer with appropriate reasoning.
(1) Part (a)
(2) Part (b)
(3) Part (c)
(4) Part (d)