3. Given the power series n=0 (n!) (2n)! an+1 (a) Simplify and find the limit, n...
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3. Given the power series n=0 (n!)² (2n)! an+1 (a) Simplify and find the limit, n→ ∞. an (b) State the radius of convergence and the endpoints. (c) There is no easy way to test the endpoints by hand. Substitute a = 4 into the series and sum it up in Python to determine if it converges or not. (d) Even that doesn't work for x =-4, but the series is alternating, so we will numerically estimate the Alternating Series Test limit. Let n= [10, 100, 1000, 10000] and use list comprehension to evaluate la, at these values. Based on this answer and your answer to (e), state the interval of convergence of the series. (e) Using the power series, plot 8₁, 83, and so on the same axes. Use your interval of conver- gence as the domain. 3. Given the power series n=0 (n!)² (2n)! an+1 (a) Simplify and find the limit, n→ ∞. an (b) State the radius of convergence and the endpoints. (c) There is no easy way to test the endpoints by hand. Substitute a = 4 into the series and sum it up in Python to determine if it converges or not. (d) Even that doesn't work for x =-4, but the series is alternating, so we will numerically estimate the Alternating Series Test limit. Let n= [10, 100, 1000, 10000] and use list comprehension to evaluate la, at these values. Based on this answer and your answer to (e), state the interval of convergence of the series. (e) Using the power series, plot 8₁, 83, and so on the same axes. Use your interval of conver- gence as the domain.
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Answer rating: 100% (QA)
a Simplify and find the limit The power series is given by 2nn2 We can simplify this by noting that 2nn22nn Therefore the power series can be written ... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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