Yeah, this comic basically explains what I do when I'm terribly bored, except that I don't have dreams that are half as imaginative as that (my dreams are often just random numbers flying around, or seeing a building in R

^{3}and trying to get to the pith floor (or something like that).)

karst wrote:capncanuck wrote:Comic implies that:

[math]\lim_{n \to \infty}\sum_{i=0}^n\frac{1}{P_i}=\infty[/math]

where [imath]P_i[/imath] is a function that generates prime numbers.

Seems straight forward to me as:

[math]\lim_{n \to \infty}\sum_{i=0}^n\frac{1}{i}=\infty[/math]

is also true.

This won't work. It's true (and not hard to prove) that the harmonic series of natural numbers diverges (your second formula). However, this doesn't necessarily imply that the harmonic series of any subset of the natural numbers diverges. For instance, [math]\sum_{n=1}^\infty \frac{1}{n^2}[/math] converges. You have to work harder to show that the harmonic series of primes diverges.

Edit: Sigh... summand and index did not match.

Isn't that a depleted harmonic series?

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This one makes me feel less alone in this world...