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Find the radius and interval of convergence of power series

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1. Find the radius of convergence and interval of convergence of series.

2. A function f is defined by f(x) = 1+ 2x + x^2 + 2x^3 +x^4+...... that is, its coefficients are =1 and =2 for all n> =0. Find the interval of convergence of the series and find an explicit formula for f(x).

3. Suppose the radius of convergence of the power series is R. What is the radius of convergence of the power series ?

See attached file for full problem description.

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It demonstrates how to find the radius of convergence and interval of convergence of power series. The solution received ''5/5'' from the student who posted the questions.

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