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Calculus 2: Power series and representations of functions

Using the ratio test, determine the intervals of convergence for the power series 28 29. Answer: The interval of convergence is 2<x<42 < x < 4.

Determine the interval of convergence for the power series n=0xnn!\sum_{n=0}^{\infty} \frac{x^n}{n!} using the ratio test.

Determine the interval of convergence for the power series: 1n(x2)n\sum \frac{1}{n} (x - 2)^n.

Find the interval of convergence for the power series with cn=1n!c_n = \frac{1}{n!} and (x2)n(x - 2)^n.

Determine the radius of convergence for the power series with cn=n!c_n = n! and (x2)n(x - 2)^n.

Express 11+x2\frac{1}{1 + x^2} as the sum of a power series.

Find the interval and radius of convergence for the power series representation of 11+x2\displaystyle \frac{1}{1+x^2}.

Find a power series representation for f(x)f(x) and determine the interval of convergence.