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))#