I think I miss something...
What I did is wrong, however I figured out what was wrong and no further help is needed.
If someone is interested I'll post the right proof. (I've used "Dirichlet Convergence Test" with "Fundamental Theorem of Calculus").
I must be mistaken, but I don't know where. Could you please correct me?:
* int(f(x), x=1..infinity) converges is equivalent to int(abs(f(x)),x=1..infinity) coonverges;
*for x>=1, f(x)/x<=f(x).
*then, int(f(x)) converges implies int(f(x)/x) converges.
This is true only if, integral (f(x)dx) from 1 to infinity, is absolutely convergent.
For example, integral (cosx/x) from 1 to infinity, is convergent but, integral abs(cosx/x) from 1 to infinity diverges.
I would be very interested in your proof, if you don't mind then...
thank you for your proof estro.
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