# Taylor expansion of sqrt(1-x)

Input interpretation |
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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 |