The majorant criterion says if a series in a Banach space has a convergent majorant, then it converges absolutely. My question is, what if a series in a Banach space has a convergent minorant, does it converges? Or, what if a series in a Banach space has a divergent majorant, does it diverges? Thank you for help.
2026-03-27 14:10:36.1774620636
The majorant/minorant criterion
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Do you understand the definitions of majorant and minorant?
In any case, the following two statements are true:
But don't just take my word for it; the proofs are extremely simple (and so I leave it as an exercise for you) and will perhaps help you see why the majorant criterion is true.