Find the Maclaurin series for f(x)=x^2/(1−8x^8). x^2/(1−8x^8)=sum_(n=0)^(oo) [_______________]

Leila Jennings 2022-07-21 Answered
From Rogawski E T 2 e section 10.7, exercise 4.
Find the Maclaurin series for f ( x ) = x 2 1 8 x 8 .
x 2 1 8 x 8 = n = 0 [ _______________ ]
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Answers (2)

tykoyz
Answered 2022-07-22 Author has 17 answers
Notice 1 1 x = x n . Hence
x 2 1 8 x 8 = x 2 ( 8 x 8 ) n = 8 n x 8 n + 2
and this is valid for | 8 x 8 | < 1
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Hayley Bernard
Answered 2022-07-23 Author has 5 answers
What you have got is almost the right answer.
x 2 1 8 x 8 = x 2 n = 0 ( 8 x 8 ) n = n = 0 8 n x 8 n + 2
, which is valid if | 8 x 8 | < 1,hence, | x | < 1 8 1 / 8
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