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Question Number 192737 by Mastermind last updated on 25/May/23

$$\mathrm{Prove}\mathrm{that}\mathrm{the}\mathrm{sequence}\left\{{\mathrm{a}}_{\mathrm{n}}\right\}\mathrm{is}\mathrm{null}$$$$\mathrm{when}\left\{{\mathrm{a}}_{\mathrm{n}}\right\}\mathrm{is}\mathrm{given}\mathrm{by}\frac{{\mathrm{n}}^3+{2\mathrm{n}}^2-1}{{\mathrm{n}}^4-{\mathrm{n}}^2+2}$$$$$$$$\mathrm{Help}!$$

Answered by Rajpurohith last updated on 26/May/23

$$clearly,\mid a_n\mid =\mid \frac{n^3+2n^2-1}{n^4-n^2+2}\mid <\mid \frac{n^3+2n^2}{n^4-n^2}\mid =\mid \frac{n+2}{n^2-1}\mid \to 0$$$$hence{a}_n\to 0$$$$$$

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