Taylor Series Expansion as x→∞?
I know that the Taylor Series formula is:
f(x) = Σ[n=0,∞] fⁿ(x₀) * (x - x₀)ⁿ / n!
However, what if I want to take the Taylor Series as x tends towards infinity? ∴ x₀ = ∞, and this formula becomes nonsensical. Is there a specific formula to perform this operation?
Example:
I have the function:
f(x) = 1/√[1 - 1/(4x²)]
When I ask Wolfram for the Taylor Series, it gives me:
1 + 1/(8x²) + 3/(128x^4) + ...
[Source: http://www.wolframalpha.com/input/?i=taylor+series+%281+-+1%2F%284x%5E2%29%29%5E%28-1%2F2%29 ]
How did they get this answer?