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...
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