TEAM PROJECT. Radius of Convergence. (a) Formula (6) for R
Chapter 15, Problem 15.2(choose chapter or problem)
TEAM PROJECT. Radius of Convergence. (a) Formula (6) for R contains iOn/On+li, not iOn+l/Oni. How could you memorize this by using a qualitative argument?(b) Change of coefficients. What happens toR (0 < R < 00) if you (i) multiply all On by k * O.(ii) multiply On by k fl * O. (iii) replace On by lion?(c) Example 6 extends Theorem 2 to nonconvergentcases of O .. /On+l' Do you understand the principle of"mixing" by which Example 6 was obtained? Use thisprinciple for making up further examples. (d) Does there exist a power series in powers of z thatconverges at z = 30 + 10i and diverges at z = 31 - 6i?(Give reason.)
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