1. ## binomial series

f (x) = ( 3 = 2x ) power -3 , vertical line x vertical line < 3 over 2
find the bionomial expansion of f(x) , in ascending powers of x , as far as the term in x POWER 3
GIVE EACH COEFFICIENT AS A SIMPLIFIED FRACTION

2. Originally Posted by cvmsmaths
f (x) = ( 3 = 2x ) power -3 , vertical line x vertical line < 3 over 2
find the bionomial expansion of f(x) , in ascending powers of x , as far as the term in x POWER 3
GIVE EACH COEFFICIENT AS A SIMPLIFIED FRACTION
Use the fact that $\frac1{(3 + 2x)^3} = \frac1{27} \frac1{(1 + \frac{2x}3)^3}$ and Newton's Binomial Identity:

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