document.write( "Question 982142: prove that. in a geometric series which has a sum to infinity. each term bears a constant ratio to the sum of all the following terms \n" ); document.write( "

Algebra.Com's Answer #603096 by Edwin McCravy(20056) $\"\"$ $\"About$

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prove that. in a geometric series which has a sum to infinity. each term bears a
\n" ); document.write( "constant ratio to the sum of all the following terms
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document.write( "We use  where \"a\" = the first term and r = the\r\n" );
document.write( "common difference:\r\n" );
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document.write( "Suppose the series is \r\n" );
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document.write( "The sum of all the terms following arⁿ⁺¹, using the formula is\r\n" );
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document.write( "We want to show that the ratio of the nth term  to the sum of all\r\n" );
document.write( "the following terms  is a constant:\r\n" );
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document.write( "That ratio is found by dividing:\r\n" );
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document.write( "   =\r\n" );
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document.write( "   =\r\n" );
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document.write( "That simplifies to \r\n" );
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document.write( " r(1-r) which is a constant.\r\n" );
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document.write( "So we have proved the proposition.\r\n" );
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document.write( "Edwin

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