Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Question #cf120

1 Answer

Aug 23, 2017

The answer is #=1+1/2x^2-1/8x^4+1/16x^6+......#

Explanation:

The Taylor series is

#(1+x)^n=1+n/(1!)x+(n(n-1))/(2!)x^2+(n(n-1)(n-2))/(3!)x^3+...#

Therefore,

#(1+x^2)^(1/2)=1+1/2x^2+((1/2)*(-1/2))/2x^4+......#

#=1+1/2x^2-1/8x^4+1/16x^6+......#

Related questions

See all questions in Constructing a Taylor Series

Impact of this question

1468 views around the world

You can reuse this answer
Creative Commons License