Binomial theorem for any index:
(1+x)n = 1+ nx +![1436_Binomial theorem for any index.png](https://www.expertsmind.com/../CMSImages/1436_Binomial theorem for any index.png)
Observations:
- Expansion is valid only when -1 <x <1
- General part of the series (1+x)-n = Tr+1 = (-1)r
xr
- General part of the series (1-x)-n = Tr+1 =
xr
- If first term is not 1, then create first term unity in the given way:
(a+ x)n = an(1+x/a)n if
< 1
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