Home/Calculus II/Sequences and series/Alternating seriesSection 14.8Alternating seriesIf bn≥0b_n\ge0bn≥0, bn+1≤bnb_{n+1}\le b_nbn+1≤bn from some point on, and bn→0b_n\to0bn→0, thenFormulaCopy LaTeX∑n=1∞(−1)n−1bn\sum_{n=1}^{\infty}(-1)^{n-1}b_nn=1∑∞(−1)n−1bnView detail →converges.Truncation error:Copy LaTeX∣RN∣≤bN+1.|R_N|\le b_{N+1}.∣RN∣≤bN+1.View detail →