Let be a convergent series. Let be the nth partial sum of the above series. Then . Should this be obvious? I don't get it.
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It might help to note that ...
Reverse the order of summation?
It makes sense when you write out the terms.
Originally Posted by Random Variable Let be a convergent series. Let be the nth partial sum of the above series. Then . Should this be obvious? I don't get it. I think you're overthinking this, by definition assuming all the proper conditions are met the Cauchy Product says that
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