Recent content by Dimwitted_UniStudent
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Undergrad Harmonic series Ʃ1/n diverges but p-series Ʃ(1/n)^p diverges?
Ok I think I get it. I consider the improper integral, if p is 1 I have ln(M) so the series diverges as the limit of M--> +∞ of the integer is ln(+∞)=+∞, if I have p > 1 I have the improper integral of 1/(x^p) or x^-p, so {[M^(1-p)]-1}/(1-p), for M--> +∞ I have a (+∞)^-k (as 1-p <0) so (zero...- Dimwitted_UniStudent
- Post #3
- Forum: Calculus
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Undergrad Harmonic series Ʃ1/n diverges but p-series Ʃ(1/n)^p diverges?
Maybe it's obvious why and I'm just dumb, but I hope you can help me understand this -----------------------------+∞ I sorta get why the Ʃ(1/n) diverges to +∞ -------------------------------n=1 ------------------+∞ But why the Ʃ(1/n)^p (p>1), converges? ------------------n=1- Dimwitted_UniStudent
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- Calculus
- Replies: 4
- Forum: Calculus