MathDB

Consider an infinite series whose

n

-th term is \pm (1\slash n), the

\pm

signs being determined according to a pattern that repeats periodically in blocks of eight (there are

2^{8}

possible patterns).
(a) Show that a sufficient condition for the series to be conditionally convergent is that there are four "

+

" signs and four "

-

" signs in the block of eight signs. (b) Is this sufficient condition also necessary?

Problem Statement