Mr. Integral
Math notes/Calculus II/Sequences and Series

Alternating Series and Error Control — Cheat sheet

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Core rule

Decreasing nonnegative bn→0b_n\to0 implies convergence of ∑(−1)nbn\sum(-1)^nb_n, with ∣RN∣≤bN+1|R_N|\le b_{N+1}.

Watch for

Absolute and conditional convergence are different. Check monotonicity before using a next-term error bound.