Difference between revisions of "009C Sample Final 3, Problem 6"
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<span class="exam"> Consider the power series | <span class="exam"> Consider the power series | ||
| − | ::<math>\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}</math> | + | ::<math>\sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}.</math> |
<span class="exam">(a) Find the radius of convergence of the above power series. | <span class="exam">(a) Find the radius of convergence of the above power series. | ||
Latest revision as of 15:21, 3 December 2017
Consider the power series
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=0}^\infty (-1)^n \frac{x^{n+1}}{n+1}.}
(a) Find the radius of convergence of the above power series.
(b) Find the interval of convergence of the above power series.
(c) Find the closed formula for the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)} to which the power series converges.
(d) Does the series
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=0}^\infty \frac{1}{(n+1)3^{n+1}}}
converge?