How do I find the $n$ th term of a binomial expansion?

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Answer 1 · 2015-07-13T20:40:09

The $n$ th term (counting from $1$ ) of a binomial expansion of $(a+b)^m$ is:

$((m),(n-1))a^(m+1-n)b^(n-1)$

$((m),(n-1))$ is the $n$ th term in the $(m+1)$ th row of Pascal's triangle.

To calculate $((p), (q))$ you can use the formula:

$((p), (q)) = (p!)/(q!(p-q)!)$

or you can look at the $(p+1)$ th row of Pascal's triangle and pick the $(q+1)$ th term.

The $(p+1)$ th row consists of the values of:

$((p), (0))$ , $((p), (1))$ , $((p), (2))$ ,..., $((p),(p))$

How do I find the nnth term of a binomial expansion?