Taylor series of sqrt(1+x)

Taylor series 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(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)

Leave a Reply

Your email address will not be published. Required fields are marked *