document.write( "Question 417410: for each series, determine if the series converges or diverges. list at least the first 5 partial sums for each series. if the series converges, state the value. show graphical support for you conclusions.\r
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Algebra.Com's Answer #292248 by richard1234(7193) $\"\"$ $\"About$

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I think you're implying the sum $\"sum%28%281%2F%28k-1%29%21%29%2C+k=1%2C+infinity%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "We can use the ratio test. We wish to show that\r
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\n" ); document.write( "\n" ); document.write( " $\"lim%28k-%3Einfinity%2C+abs%28%281%2Fk%21%29%2F%281%2F%28k-1%29%21%29%29%29\"$ exists and is less than 1. This limit is equal to\r
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\n" ); document.write( "\n" ); document.write( "Hence, the series converges. If you know the Taylor series $\"e%5Ex+=+sum%28%28x%5Ek%29%2Fk%21%2C+k=0%2Cinfinity%29\"$ and that the sums $\"sum%28%281%2F%28k-1%29%21%29%2C+k=1%2C+infinity%29\"$ and $\"e%5Ex+=+sum%28%28x%5Ek%29%2Fk%21%2C+k=0%2Cinfinity%29\"$ are equivalent when x=1, we conclude that the series converges to $\"e\"$ . \n" ); document.write( "

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