Series of Constants JSFH

JSFH Determine if the series 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 converges or diverges. If it converges, determine its value. JSFH

JSFH Try the Ratio test. 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 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, where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiQtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRjQ2JVEia0YnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRkIvJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRkI= is a sequence of positive constants: General Term LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRImtGJ0YyRjUvRjZRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSC8lKXN0cmV0Y2h5R0ZILyUqc3ltbWV0cmljR0ZILyUobGFyZ2VvcEdGSC8lLm1vdmFibGVsaW1pdHNHRkgvJSdhY2NlbnRHRkgvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZXRj0= 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

KiQpIiIkSSZfX2tfX0c2IiEiIg==

Test Number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy 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

IyIiIiIiJA==

JSFH If necessary, try the Integral test. Expression palette: Definite integral template Construct and evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkobXN1YnN1cEdGJDYnLUkjbW9HRiQ2LVErJkludGVncmFsO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R1EldHJ1ZUYnLyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZHLUYjNiUtSSNtbkdGJDYkUSIxRidGMi8lMGZvbnRfc3R5bGVfbmFtZUdRJVRleHRGJ0YyLUYjNiUtRi82LVEoJmluZmluO0YnRjIvRjZRJmZhbHNlRicvRjlGWS9GO0ZZL0Y+RlkvRkBGWS9GQkZZL0ZERllGRUZIRlBGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGXG8tSSNtaUdGJDYlUSJmRicvJSdpdGFsaWNHRjwvRjNRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRmBvNiVRInhGJ0Zjb0Zlb0ZQRjJGMi1GLzYtUSJ+RidGMkZYRlpGZW5GZm5GZ25GaG5GaW5GRUZILUYvNi5RMCZEaWZmZXJlbnRpYWxEO0YnRmNvRmVvRjVGOC9GO0Y3Rj0vRkBGN0ZBRkNGRUZIRlxwRlBGMg== where 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 JSFH JSFH JSFH JSFH

JSFH Control-drag the series. Context Menu: Evaluate and Display Inline JSFH JSFH To obtain this value from "first principles," recognize the series as linear combination of two geometric series, that is, as 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 and note that the sum of the geometric series 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 is 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, so that 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. JSFH JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Obtain 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, the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=th partial sum Generate a sequence of partial sums Control-drag the general term of the series. Press the Enter key. Context Menu: Constructions\342\211\273Sum\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= 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 Context Menu: Evaluate (from inert) Context Menu: Sequence\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= 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 Context Menu: Conversions\342\211\273To List Context Menu: Approximate\342\211\2735 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Graph the sequence of partial sums Form the list 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 (using the equation label). Press the Enter key. Context Menu: Sequence\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= 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 Context Menu: Conversions\342\211\273To List Context Menu: Plots\342\211\273Plot Builder LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Obtain the limit of the sequence of partial sums Expression palette: Limit operator Obtain 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH