text: ## 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.
explanation: The document contains a mathematical problem and its solution. It evaluates the limit of a sequence and uses the Sandwich Theorem to show that the sequence is convergent and its limit is 0.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a mathematical problem and its solution. It evaluates the limit of a sequence and uses the Sandwich Theorem to show that the sequence is convergent and its limit is 0.
  
  Label: question-and-answer