text: 1. ## counting query
  
  Can anyone help me find the sixth term of $\displaystyle \left( x - \frac{1}{2}\right)^{10} ?$
  
  Thanks.
  
  2. Originally Posted by 14041471
  Find the sixth term of (x – ½)10
  A quick way (and probably the simplest way) is to apply the Binomial Theorem. To find the m-th term of a binomial with first term "a", second term "b", and power "n", use:
  
  . . . . .$\displaystyle \frac{n!}{m!(n\, -\, m)!}\, a^{n-m} b^{m}$
  
  Note: Remember to count the first term as "m = 0", so "the sixth term" is really "m = 5".
  
  . . . . .$\displaystyle \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}$
explanation: The document contains a math question and a detailed answer to that question. The question asks for the sixth term of the binomial expansion \(\left( x - \frac{1}{2}\right)^{10}\), and the answer provides a step-by-step method using the Binomial Theorem.
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. ## counting query
  
  Can anyone help me find the sixth term of $\displaystyle \left( x - \frac{1}{2}\right)^{10} ?$
  
  Thanks.
  
  2. Originally Posted by 14041471
  Find the sixth term of (x – ½)10
  A quick way (and probably the simplest way) is to apply the Binomial Theorem. To find the m-th term of a binomial with first term "a", second term "b", and power "n", use:
  
  . . . . .$\displaystyle \frac{n!}{m!(n\, -\, m)!}\, a^{n-m} b^{m}$
  
  Note: Remember to count the first term as "m = 0", so "the sixth term" is really "m = 5".
  
  . . . . .$\displaystyle \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer to that question. The question asks for the sixth term of the binomial expansion \(\left( x - \frac{1}{2}\right)^{10}\), and the answer provides a step-by-step method using the Binomial Theorem.
  
  Label: question-and-answer