6. Suppose that the radius of convergence of the power series ? c_n x^n is R. What is the radius of convergence of the power series ? c_n x^{7n}? Justify your answer.
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The radius of convergence R is the value such that the power series converges for all |x| < R and diverges for all |x| > R. Now, consider the power series C_nx^{7n}. We can rewrite this series as (C_nx^7)^n. Let y = x^7, then the series becomes C_ny^n. Since the Show more…
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