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AceK
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Power Series Representation of a Function when "r" is a polynomial
Find a power series representation for the function and determine the radius of convergence.
f(x)=[tex]\stackrel{(1+x)}{(1-x)^{2}}[/tex]
a series converges when |x|<1;
[tex]\stackrel{a}{1-r}[/tex]=[tex]\sum[/tex]a(r)[tex]^{n}[/tex]
I got the power series of [tex]\sum[/tex](1+x)(2x-x^2)[tex]^{n}[/tex] by expanding the denominator of the function and getting it into geometric series form; I then converted it to a series using the above equation. The answer given in my book is [tex]\sum(2n+1)x^{n}[/tex], which seems more correct; also, the radius of convergence is much easier to determine with their answer. How do they arrive at this answer?
Homework Statement
Find a power series representation for the function and determine the radius of convergence.
f(x)=[tex]\stackrel{(1+x)}{(1-x)^{2}}[/tex]
Homework Equations
a series converges when |x|<1;
[tex]\stackrel{a}{1-r}[/tex]=[tex]\sum[/tex]a(r)[tex]^{n}[/tex]
The Attempt at a Solution
I got the power series of [tex]\sum[/tex](1+x)(2x-x^2)[tex]^{n}[/tex] by expanding the denominator of the function and getting it into geometric series form; I then converted it to a series using the above equation. The answer given in my book is [tex]\sum(2n+1)x^{n}[/tex], which seems more correct; also, the radius of convergence is much easier to determine with their answer. How do they arrive at this answer?
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