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**Unformatted text preview: **to find out. Question B: (optional) The book's theorem on alternating series says: IF b_n is decreasing AND lim b_n = 0 THEN the series converges. It does *not* say: If either of those conditions fails, then the series diverges. i) Can you find a b_n (all terms >= 0 ) where it's sometimes increasing and sometimes decreasing (all the way to infinity), and the series (-1)^n b_n converges? ii) Can you find a b_n that is purely decreasing, but whose limit is not 0, for which the series still converges? iii) Any other similar explorations?...

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