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".

. . . . .$\displaystyle \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}$
The text contains a mathematical question about finding the sixth term of a binomial expansion, and an answer is provided using the Binomial 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
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".

. . . . .$\displaystyle \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}$
user
The text contains a mathematical question about finding the sixth term of a binomial expansion, and an answer is provided using the Binomial Theorem.

TYPE: SINGLE_QUESTION_WITH_ANSWER