Ratio Test Series of Positive Constants JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 4-34</Text-field> JSFH Use the Ratio test to determine if the series 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 converges.
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<Text-field style="Heading 1" layout="Heading 1"><Taskdata-inline tag_id="2"><Font style="Heading 1">Solution by Task Template</Font></Taskdata-inline></Text-field> JSFH Control-drag the general term of the series. Press the Enter key. JSFH Tools\342\211\273Tasks\342\211\273Browse: Calculus - Integral\342\211\273Series\342\211\273Ratio Test
Ratio Test for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkrbXVuZGVyb3ZlckdGJDYnLUkjbW9HRiQ2LVEmJlN1bTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictRiM2JC1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dGPC9GM1EnaXRhbGljRidGMi1GIzYkLUYvNi1RKCYjODczNDtGJ0YyL0Y2USZmYWxzZUYnL0Y5RmVuL0Y7RmVuL0Y+RmVuL0ZARmVuL0ZCRmVuL0ZERmVuRkUvRklGR0YyRltvLyUsYWNjZW50dW5kZXJHRmVuLUklbXN1YkdGJDYlLUZONiVRImFGJ0ZRRlNGSy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjI=, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiQtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRjQ2JVEia0YnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRkIvJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRkI= is a se\011\011quence of positive constants: General Term LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImtGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXRj0= 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 KiQpIiIkSSZfX2tfX0c2IiEiIg== Test Number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy 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 IyIiIiIiJA==
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<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field> JSFH Define LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImtGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn as a function of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= Write the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImtGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUZANi1RKSZoZWxsaXA7RidGPUZDRkZGSEZKRkxGTkZQL0ZTUSwwLjE2NjY2NjdlbUYnL0ZWRmVuRj0= Context Menu: Assign Function JSFH Obtain the limit of the ratio 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 Expression palette: Limit operator Form 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 Context Menu: Evaluate and Display Inline JSFH
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