Find the binomial series representation for \( \frac{2}{\sqrt{1-x}} \). What is the value of the coefficient to \( x^{2} \) in this expansion? (Give your answer as a decimal, rounded to 3 places if needed). \( \square \)
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Step 1: Recall the binomial series expansion for \((1 + x)^n\), which is given by: \[ (1 + x)^n = \sum_{k=0}^{\infty} \binom{n}{k} x^k \] where \(\binom{n}{k} = \frac{n(n-1)(n-2)\cdots(n-k+1)}{k!}\). Show more…
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