x-n-1-n-n-10-n-2-1-n-N-show-if-the-sequence-is-limited-

Question Number 109765 by Karani last updated on 25/Aug/20

(x_{n}) = \frac{{(- 1)}^{n} n + 10}{\sqrt{n^{2} + 1}}, n \in N show if the sequence is limited .

Answered by mathmax by abdo last updated on 25/Aug/20

∣ x_{n} ∣ ⩽ \frac{n + 10}{\sqrt{n^{2} + 1}} we have \sqrt{n^{2} + 1} > n \Rightarrow \frac{1}{\sqrt{n^{2} + 1}} < \frac{1}{n} \Rightarrow

∣ x_{n} ∣< \frac{n + 10}{n} = 1 + \frac{10}{n} ⩽ 11 \Rightarrow (x_{n}) is limited