Question

6th term of expansion (1+x)^32
quickest method

Answer 1

for a binomial

\[(1+ x)^n = \sum_{r = 0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right) 1^{n - r}x^r\]

so to find the 6th term let r = 5

remember the terms start at r = 0 0, 1, 2, 3, 4, 5

and evaluate

\[\left(\begin{matrix}32 \\ 5\end{matrix}\right) 1^{32-5}\times x^5\]

Answer 2

And what if the terms were (a+b) instead of (1+x)

Answer 3

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