Question Number 142492 by leesjyons last updated on 01/Jun/21
$$\mathrm{Prove}\:\mathrm{that}\:\underset{{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}}{\mathrm{3}{n}^{\mathrm{2}} \:+\:\mathrm{2}}\:\mathrm{diverges}. \\ $$
Answered by mathmax by abdo last updated on 02/Jun/21
$$\mathrm{dvergence}\:\mathrm{clear}\:\mathrm{due}\left[\mathrm{to}\:\:\frac{\mathrm{n}}{\mathrm{3n}^{\mathrm{2}} \:+\mathrm{2}}\sim\frac{\mathrm{1}}{\mathrm{3n}}\:\left(\mathrm{n}\sim\infty\right)\:\mathrm{and}\:\Sigma\:\frac{\mathrm{1}}{\mathrm{3n}}\mathrm{dv}\right. \\ $$