express the function as a power series (exoress your answers in sigma notation) and find the radius of convergence)
f(x) = 1 / [ (x^6)+1 ]
engeering maths taylor series?
2013-10-21 2:55 am
回答 (1)
2013-10-21 3:20 am
✔ 最佳答案
Use the geometric series 1/(1 - t) = Σ(n = 0 to ∞) t^n, convergent for |t| < 1.
Let t = -x^6:
1/(1 - (-x^6)) = Σ(n = 0 to ∞) (-x^6)^n, convergent for |-x^6| = |x|^6 < 1.
==> 1/(x^6 + 1) = Σ(n = 0 to ∞) (-1^n x^(6n), convergent for |x| < 1.
(So, the radius of convergence is 1.)
I hope this helps!
收錄日期: 2021-04-11 20:10:11
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