#13) Find the radius and interval of convergence of the power series (Sigma∞ n=1) (−1)^n(x −...

#13) Find the radius and interval of convergence of the power series (Sigma∞ n=1) (−1)^n(x − 1)^n/n4^n by responding to the following sequence of questions.

(a) Compute the limit L = lim n→∞ |an+1|/|an| .

(b) Given that the power series absolutely converges for L < 1 by the Ratio Test, compute the radius of convergence, where the radius of convergence is the real number R such that the power series converges for all |x| < R.

(c) Test whether the power series is convergent at the endpoints of the interval determined by R to compute the interval of convergence.

Expert Solution

milcah answered 2 years ago

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#13) Find the radius and interval of convergence of the power series (Sigma∞ n=1) (−1)^n(x −...

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