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Question Number 32933 by abdo imad last updated on 06/Apr/18

Σ u_n  is a convergent serie with positif terms  find the nature of  Σ_(n≥1)  ((√u_n )/n)  and   Σ_(n≥o)   (u_n /(1+u_n ))  .

$$\Sigma\:{u}_{{n}} \:{is}\:{a}\:{convergent}\:{serie}\:{with}\:{positif}\:{terms} \\ $$$${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}\geqslant\mathrm{1}} \:\frac{\sqrt{{u}_{{n}} }}{{n}}\:\:{and}\:\:\:\sum_{{n}\geqslant{o}} \:\:\frac{{u}_{{n}} }{\mathrm{1}+{u}_{{n}} }\:\:. \\ $$

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