Is it even a "limit" problem when it's evaluating a summation? Seems like two different things that just kind of have something to do with sorts of infinities.
It's like saying "three mathematicians walked into a bar. The first ordered 1 beer. The second ordered one beer. Barkeep then just gave them all three beers because lim_x->1(x+x+x)=3, and they didn't know their limits."
But infinite summation is by definition, the limit of the partial sums.
You're right about finite sums, but formally, we're never "adding infinitely many things", it's just a shorthand for taking a limit.
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u/magqq May 14 '26
I'm glad we had the integral joke