What is an alternating series? an alternating series is a whose terms are. under what conditions does an alternating series converge? an alternating series sigma^infinity_n=1 a_n = sigma^infinity_n=1 (-1)^n-1 b_n, where b_n = |a_n|, converges if 0 < b_n+1 lessthanorequalto b_n for all n, and lim_n rightarrow infinity b_n =. if these conditions are satisfied, what can you say about the remainder after n terms? the error involved in using the partial sum s_n as an approximation to the total sum s is the r_n = s - s_n and the size of the error is b_n+1.