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 |