text: 1. ## Riemman Sum
  
  The limit as x approches infinity of the sum from i=1 to n of :
  
  $(1+\frac{i}{n})^3$
  
  2. ## Divergent
  
  $\lim_{n\rightarrow\infty}\sum_{i=1}^n(1+\frac{i}{n })^3$ = $\lim_{n\rightarrow\infty}\sum_{i=1}^n\frac1{n^3}(n ^3+3n^2i+3ni^2+i^3)$= $\lim_{n\rightarrow\infty} 1+\frac3n\sum_{i=1}^ni+\frac3{n^2}\sum_{i=1}^ni^2+ \frac3{n^3}\sum_{i=1}^ni^3$ = $\lim_{n\rightarrow\infty} 1+\frac3n\frac{n(n+1)}2+\frac3{n^2}\frac{n(n+1)(2n +1)}6+\frac3{n^3}\frac{n^2(n+1)^2}4$ = $\infty$
  
  This limit diverges. What was the original problem?
explanation: The document contains a math problem involving a Riemann sum and its evaluation. It also includes a detailed solution showing that the limit diverges. The document ends with a question asking about the original problem.
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: 1. ## Riemman Sum
  
  The limit as x approches infinity of the sum from i=1 to n of :
  
  $(1+\frac{i}{n})^3$
  
  2. ## Divergent
  
  $\lim_{n\rightarrow\infty}\sum_{i=1}^n(1+\frac{i}{n })^3$ = $\lim_{n\rightarrow\infty}\sum_{i=1}^n\frac1{n^3}(n ^3+3n^2i+3ni^2+i^3)$= $\lim_{n\rightarrow\infty} 1+\frac3n\sum_{i=1}^ni+\frac3{n^2}\sum_{i=1}^ni^2+ \frac3{n^3}\sum_{i=1}^ni^3$ = $\lim_{n\rightarrow\infty} 1+\frac3n\frac{n(n+1)}2+\frac3{n^2}\frac{n(n+1)(2n +1)}6+\frac3{n^3}\frac{n^2(n+1)^2}4$ = $\infty$
  
  This limit diverges. What was the original problem?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math problem involving a Riemann sum and its evaluation. It also includes a detailed solution showing that the limit diverges. The document ends with a question asking about the original problem.
  
  Label: question-and-answer