Power Series Radius of Convergence JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 4-38</Text-field> JSFH Obtain the radius of convergence of the series 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.
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution by Task Template</Text-field> JSFH Control-drag the general coefficient. Press the Enter key. JSFH Tools\342\211\273Tasks\342\211\273Browse: Calculus - Integral\342\211\273Series\342\211\273Radius of Convergence Reference LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImtGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn by its equation label. The value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is 2.
Ratio-Test Method for Radius of Convergence of 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LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y5USdub3JtYWxGJ0YrRjs= and LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUScmIzk1NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGK0Y4 fixed integers, LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y5USdub3JtYWxGJ0YrRjs= and LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1JJW1zdWJHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYwNiQtRiw2JVEia0YnRjhGOy9GPFEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZDRitGQw== positive: General term LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1JJW1zdWJHRiQ2JS1GLDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYwNiQtRiw2JVEia0YnRjhGOy9GPFEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZDRitGQw== 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 KiQtSSpmYWN0b3JpYWxHJSpwcm90ZWN0ZWRHNiNJJl9fa19fRzYiISIi Enter LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y5USdub3JtYWxGJ0YrRjs=, the coefficient of LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUSJrRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y5USdub3JtYWxGJ0YrRjs= in the power of LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JC1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y5USdub3JtYWxGJ0YrRjs= in the general term: LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNictSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JkYrLUkobWFjdGlvbkdGJDYkLUYwNidGKy1GMDYkLUkjbW5HRiQ2JVEiMkYnLyUrZm9yZWdyb3VuZEdRK1s5NSwwLDIxN11GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGQEYrLyUscGxhY2Vob2xkZXJHUSV0cnVlRidGQC8lK2FjdGlvbnR5cGVHUTttYXBsZXNvZnQ6dGFzay1wbGFjZWhvbGRlckYnRitGQEYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGQA== IiIj Radius of Convergence 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 SSlpbmZpbml0eUclKnByb3RlY3RlZEc=
LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNictSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGMg== LUknbXN0eWxlRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YnNiYtSSNtaUdGJDYjUSFGJy1JJW1yb3dHRiQ2JEYrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjI=JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ratio test from first principles Write 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 Context Menu: Assign Function JSFH Write 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 and press the Enter key. Context Menu: Simplify\342\211\273Simplify Context Menu: Limit\342\211\273k\342\211\273\342\210\236\342\211\273left Isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiQtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y4USdub3JtYWxGJ0Y6LyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRj5GOg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH