(a) Use Equation 1 to find a power series representation for . What is the radius of convergence?
(b) Use part (a) to find a power series for .
(c) By putting in your result from part (a), express as the sum of an infinite series.
i) The power series representation using Equation for the function
ii) The radius of convergence.
If the power series has radius of convergence , then the function defined by
is differentiable (and therefore continuous) on the interval and
has the radius of convergence .
Given the function
We know that,
The power series for using part (a)
as the sum of an infinite series, by putting in the result of part (a)
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