Let {an} be a monotonically decreasing sequence of positive real numbers with limit 0. Let {bn} be a rearrangement of the sequence such that for every non-negative integer m, the terms b3m+1, b3m+2, b3m+3 are a rearrangement of the terms a3m+1, a3m+2, a3m+3. Prove or give a counterexample to the following statement: the series ∑n=1∞(−1)nbn is convergent.
SequencesConvergenceSummationlimits