Series Two
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Can you give an example of two series that converge but when multiplied diverge?
two series an and bn, both converge. but an*bn diverges. give an example?
let an = ((-1)^n)(1/(n^(1/2))) and let bn = ((-1)^n)(1/(n^(1/3)))
If you don't consider "conditionally convergent series," then it can be proven that there are no two series that converge, but diverge when the terms are multiplied together.
Think, lim of an and bn as n -> infinity = 0 so (an)(bn) is always smaller than an and bn.
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