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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+......#

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