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 ∞ [ _______________ ]

Question

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              ∞        [      _______________    ]

tykoyz · Accepted Answer

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        |    &amp;lt;  1

Hayley Bernard · Accepted Answer

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        |    &amp;lt;  1,hence,       |    x      |    &amp;lt;      1          8              1                  /                8

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

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