document.write( "Question 1115944: Specify the values of x for which the given infinite geometric series has a sum. Then find the sum in terms of x.
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Algebra.Com's Answer #730770 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "An infinite geometric progression\r\n" );
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document.write( "    a, ar, ar^2, ar^3, . . . \r\n" );
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document.write( "has a sum if and only if its common ratio \"r\"  has the modulus (= the absolute value)  |r| less than 1:  |r| < 1.\r\n" );
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document.write( "In your case  r = 4x,  so the condition that this geometric series does converge is\r\n" );
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document.write( "|4x| < 1,   or,  equivalently,   |x| < ,   or  -0.25 < r < 0.25.\r\n" );
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