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The other day I was showing convergence for an alternating series, let's call it ##\sum (-1)^n b_n##. I showed that ##\lim_{n \to \infty} b_n = 0## and that ##b_n## was monotonically decreasing; hence the series converges by the alternating series test. but I needed also to show it did not converge to zero. the argument I used was that since ##|b_1 - b_2| >0## and that since ##b_n## monotonically decreases, we then know ##\sum (-1)^n b_n > |b_1 - b_2|##. Is my intuition correct here? If so, is it ever possible to have a series described above converge to zero?

Let me know what you think!

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# Alternating series question

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