Question

Find the radius of convergence in two ways (a) using the Cauchy root test (or what your book calls Cauchy-Hadamard formula) (b) Using integration/differentiation and using what you know about geometric series.\\ $\sum_{n=1}^{\infty} (z+i)^{2n}$

          Find the radius of convergence in two ways (a) using the Cauchy root test (or what your book calls Cauchy-Hadamard formula) (b) Using integration/differentiation and using what you know about geometric series.\\
$\sum_{n=1}^{\infty} (z+i)^{2n}$

Find the radius of convergence in two ways (a) using the Cauchy root test (or what your book calls Cauchy-Hadamard formula) (b) Using integration/differentiation and using what you know about geometric series.

∑n=1^∞ (z+i)^2n

Added by Cynthia M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

04/24/2020

Step 1

For a power series with coefficients an, the Cauchy-Hadamard formula states that the radius of convergence R is given by: R = 1 / lim sup (|an|^(1/n)) Show more…

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I understand how to apply the root test for power series with power n, but I do not know what to do differently when there's a power of 2n. Find the radius of convergence in two ways: a) using the Cauchy root test (or what your book calls Cauchy-Hadamard formula); b) using integration/differentiation and using what you know about geometric series. u(2+2)^1 = u7.