Taylor expansion of 1+x

The Taylor seriesMathworldPlanetmath for  f(x)=1+x  using the


is given in the table below for the first few .

expansion simplified at  a=0
0 f(a) (1+a)1/2 1
1 f(a)(x-a) 12(1+a)-1/2(x-a) 12x
2 f(2)(a)2!(x-a)2 -18(1+a)-3/2(x-a)2 -18x2
3 f(3)(a)3!(x-a)3 348(1+a)-5/2(x-a)3 116x3
4 f(4)(a)4!(x-a)4 -15384(1+a)-7/2(x-a)4 -5128x4
5 f(5)(a)5!(x-a)5 1053840(1+a)-9/2(x-a)5 7256x5
6 f(6)(a)6!(x-a)6 -94546080(1+a)-11/2(x-a)6 -211024x6
Table 1: Taylor Series for f(x)=1+x

The general coefficient of the expansion, for n2 is:

f(n)(a)n! =(12n)(1+a)12-n
Title Taylor expansion of 1+x
Canonical name TaylorExpansionOfsqrt1x
Date of creation 2013-03-22 15:45:52
Last modified on 2013-03-22 15:45:52
Owner stevecheng (10074)
Last modified by stevecheng (10074)
Numerical id 11
Author stevecheng (10074)
Entry type Example
Classification msc 26A09
Related topic ExamplesOnHowToFindTaylorSeriesFromOtherKnownSeries