document.write( "Question 1041293: True or False. \r
\n" ); document.write( "\n" ); document.write( "If a sequence is convergent, then the series is convergent. If true, explain why. If false, explain why or provide a counterexample. \n" ); document.write( "

Algebra.Com's Answer #656256 by ikleyn(52793) $\"\"$ $\"About$

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\n" ); document.write( "True or False. \r
\n" ); document.write( "\n" ); document.write( "If a sequence is convergent, then the series is convergent. If true, explain why. If false, explain why or provide a counterexample.
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document.write( "    In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence.  \r\n" );
document.write( "    (Wikipedia, this article.)\r\n" );
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document.write( "False.\r\n" );
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document.write( "Classic counter-example is the harmonic sequence\r\n" );
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document.write( ", , , . . . , , . . . \r\n" );
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document.write( "The sequence is converged (to zero), but the series is divergent.\r\n" );
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