# 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(1/x)/2 – 1/8 (1/x)^(3/2) + 1/16 (1/x)^(5/2) – 5/128 (1/x)^(7/2) + O((1/x)^4) (Puiseux series) |

Approximations about x=0 up to order 3 |

(order n approximation shown with n dots) |