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References to 'Abel's lemma'
1. $\displaystyle x\log^2x=O\left(\sum_{n \le x} 2^{\Omega(n)} \right)$ by Wkbj79
2. analytic number theory by Wkbj79
3. asymptotic estimate by Wkbj79
4. Dirichlet's convergence test by lieven
5. example of summation by parts by pahio
6. inequality of logarithmic and asymptotic density by kompik