## Thomas' Calculus 13th Edition

$\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{n+3}{n^2+5n+6}$ or, $\lim\limits_{n \to \infty} \dfrac{n+3}{n^2+5n+6}= \lim\limits_{n \to \infty} \dfrac{n+3}{(n+3)(n+2)}$ Now, apply Sandwich Theorem which states that $\lim\limits_{n \to 0} \dfrac{1}{n}=0$ Thus, $\lim\limits_{n \to \infty} \dfrac{1}{n+2}=0$ Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
The passage contains a mathematical problem involving the limit of a sequence and its solution, including the application of the Sandwich Theorem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Thomas' Calculus 13th Edition

$\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} \dfrac{n+3}{n^2+5n+6}$ or, $\lim\limits_{n \to \infty} \dfrac{n+3}{n^2+5n+6}= \lim\limits_{n \to \infty} \dfrac{n+3}{(n+3)(n+2)}$ Now, apply Sandwich Theorem which states that $\lim\limits_{n \to 0} \dfrac{1}{n}=0$ Thus, $\lim\limits_{n \to \infty} \dfrac{1}{n+2}=0$ Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is convergent.
user
The passage contains a mathematical problem involving the limit of a sequence and its solution, including the application of the Sandwich Theorem.

TYPE: SINGLE_QUESTION_WITH_ANSWER