Asked by Amy
Use power series division to find the Maclaurin series for f(x) = 1/ ( 1+(x^3) ).
Answers
Answered by
Reiny
(1 + a)^n = 1^n + n(1)^(n-1)(a)
f(x) = 1/ ( 1+(x^3) )
= (1 + x^3)^-1
= 1^-1 + (-1)(1)(x^3) + (-1)(-2)/2! (x^3)^2 + (-1)(-2)(-3)/3! (x^3)^3 + (-1)(-2)(-3)(-4).4! (x^3)^4 + ...
= 1 - x^3 + x^6 - x^9 + x^12 - ......
f(x) = 1/ ( 1+(x^3) )
= (1 + x^3)^-1
= 1^-1 + (-1)(1)(x^3) + (-1)(-2)/2! (x^3)^2 + (-1)(-2)(-3)/3! (x^3)^3 + (-1)(-2)(-3)(-4).4! (x^3)^4 + ...
= 1 - x^3 + x^6 - x^9 + x^12 - ......
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