Taylor expansion of sqrt(1-x)

Taylor expansion of sqrt(1-x)

Input interpretation
series | sqrt(1 – x)
Series expansion at x=0
1 – x/2 – x^2/8 – x^3/16 – (5 x^4)/128 – (7 x^5)/256 + O(x^6)
(Taylor series)
(converges when abs(x)<1)
Series expansion at x=∞
sqrt(-x) – sqrt(-x)/(2 x) – sqrt(-x)/(8 x^2) – sqrt(-x)/(16 x^3) – (5 sqrt(-x))/(128 x^4) + O((1/x)^5)
(generalized Puiseux series)
Approximations about x=0 up to order 3
(order n approximation shown with n dots)
Series representation
sqrt(1 – x) = sum_(n=0)^infinity x^n (-1)^n binomial(1/2, n) for abs(x)<1

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