Prove-that-the-sequence-a-n-is-null-when-a-n-is-given-by-n-3-2n-2-1-n-4-n-2-2-Help-

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

Prove that the sequence {a_{n}} is null

when {a_{n}} is given by \frac{n^{3} + {2 n}^{2} - 1}{n^{4} - n^{2} + 2}

Help!

Answered by Rajpurohith last updated on 26/May/23

c l e a r l y, ∣ a_{n} ∣=∣ \frac{n^{3} + 2 n^{2} - 1}{n^{4} - n^{2} + 2} ∣<∣ \frac{n^{3} + 2 n^{2}}{n^{4} - n^{2}} ∣=∣ \frac{n + 2}{n^{2} - 1} ∣\to 0

h e n c e a_{n} \to 0