document.write( "Question 1121032: S(x)=1+5(x−5)+25(x−5)^2+125(x−5)^3+⋯.\r
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Algebra.Com's Answer #736769 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "S(x) is the sum of the infinite geometric progression with the first term of 1 and the common ratio of  r = 5*(x-5).\r\n" );
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document.write( "Such a progression converges  if and only if  |r| < 1,  which gives\r\n" );
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document.write( "|5*(x-5)| < 1,   or\r\n" );
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document.write( "|x-5| < ,   or\r\n" );
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document.write( " < x -5 < ,   or, equivalently\r\n" );
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document.write( "4.8 < x < 5.2.\r\n" );
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document.write( "Answer.  The convergence domain is  the interval  (4.8,5.2).\r\n" );
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