Recent content by coffeetheorem

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    Graduate Two divergent series whose minimum converges?

    arildno: Part of the stipulation of the problem is that both sequences must be positive and decreasing. I have edited the original post to clarify this.
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    Graduate Two divergent series whose minimum converges?

    Thanks, [SIZE="1"]boss! I had attempted a pair that was similar, but too simple and not quite workable. Here's what I initially tried (in reciprocal): a_n = 1+9+9+ 9+ 25+25+25+25+25+49+49+49+49+49+49+49+81 … (nine times) … b_n = 4+4+16+16+16+16+36+36+36+36+36+36+64 … (eight times) …...
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    Graduate Two divergent series whose minimum converges?

    I am struggling to find two divergent series, \Sigmaan and \Sigmabn, such that the series of minimum terms, \Sigmamin{an,bn}, actually converges. A further stipulation is that both an and bn must be positive, decreasing sequences. (Otherwise the problem is trivial, as one could simply...