# In each of Problems 18 through 22,3"single power series whose generic tIn each of Proble ms 7 through 13, determine the Taylor series aboutthe point xo for the given function. Also determine the radius ofconvergence of the series.0018. n(n-1) a,x-2n -27. sin x,19. xΣna,x"-1 Σ αx+Σαπ'n=1k-08. ex, xo = 0m(m - 1)am"-220.+ x9. x, xo = lm=2k=10. x2, xo = -121. nanx"-1 +xanxn=011. Inx, xo = 1n=122. xn(n-1)a,x"-2+112.1- xn=0=223.Determine the a, so that the113.1 - x+nan"-1n=114. Let y nx".is satisfied. Try to identify the fn=0a. Compute y' and write out the first four terms of the series.uand write out the first four terms of the series.Σaχ.E-E

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How do I appropriately answer number 13? This is a question from my Differential Equations course, and the name of the chapter is, "Review of Power Series." I think that to determine the radius of convergence is by doing some kind of root test, ratio test, etc.

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Step 1

We are given the function 1/(1-x). In this problem we need to find the Taylor series about the point x0 = 2. Also, we need to find the radius of convergence of the series formed.

Note:

Step 2

Here,

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