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**Paperwings** Problem

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Let $\displaystyle f(q) = \frac{1}{q} [1-(1-2q)^{-3/2}] $ (*)

Evaluate this formula for $\displaystyle q = 10^{-8} $ using the power series expansion for f at q = 0:

$\displaystyle f(q) = -3 - \frac{3*5}{3!}q - \frac{3*5*7}{3!}q^2 - .... $ (1)

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I have two questions.

1.) Is this power series expansion correct? I tried inputting this function in MATLAB and it gives me a different power series expansion:

$\displaystyle f(q) = -3-\frac{15}{2}q-\frac{35}{2}q^2- \frac{315}{8}q^3 - \frac{693}{8}q^4 ... $ (2)

2. Regarding the power series which is defined as

$\displaystyle f(q) = f(a) + f'(a)(x-a)+.... $ at q = a.

Since this power series (1) I do not understand how a power series can be derived this way since at q = 0, then f(0) from (*) is undefined because we can not divide by 0, correct?

Thank you for reading.