What's the method used to determine if a sum or product is infinite
or not?

Don't know about products. For sums:

Generally definite integration works, though it won't tell you
*exactly* what a value converges to (in which case you use a computer
to do the first thousand, and can generally see, from what I
remember).

In the case of the primes, and some other cases, its outright easy (by
the way, 1^n+2^n+3^n+... will diverge for all n >= -1, but very
slowly right at -1)

Nathan

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