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 Originally Posted by a500lbgorilla
I guess what the professor was getting at is how do you know the p-series converges by virtue of p>1? I just sat down and ran through my thinking and saw that eventually the terms add nothing to the end, but I didn't prove anything. In order to mathematically KNOW that it converges, is it enough to know that all p-series with p>1 converge or do you have to go further and be able to demonstrate for any given p-series p>1, it does converge?
the p-series rule is that it converges when p>1. my issue is when given a function that is not technically p-series (becuase it's not strictly in the form 1/n^p), but for all intents and purposes it behaves like a p-series, why can't i just say "it converges because of p-series rules"? this must mean that the logic breaks down somewhere, but i cant find where that would be. and if it doesn't, im wondering what the purpose of solving a problem by proving it is important when you could just solve the problem. is a proof actually creating something, or is it so we can say "ah we know this thing is true for all possible circumstances instead of just knowing it's true for all circumstances we've thought of"?
my professor is the type to say that "applied mathematics" is an oxymoron. makes my head explode. if something isn't applied it has no discernible value and therefore is not a relevant or assessable thing. if im wrong about this, please disabuse me of it.
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