document.write( "Question 1099656: Find the sum in the series (15/42)+(15/56)+(15/72)+(15/90)+...+(15/9900) \n" ); document.write( "
Algebra.Com's Answer #714111 by ikleyn(52781)\"\" \"About 
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document.write( "\"1%2F42\" = \"1%2F%286%2A7%29\" = \"1%2F6-1%2F7\".\r\n" );
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document.write( "\"1%2F56\" = \"1%2F%287%2A8%29\" = \"1%2F7-1%2F8\".\r\n" );
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document.write( "\"1%2F72\" = \"1%2F%288%2A9%29\" = \"1%2F8-1%2F9\".\r\n" );
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document.write( "\"1%2F90\" = \"1%2F%289%2A10%29\" = \"1%2F9-1%2F10\".\r\n" );
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document.write( "All your terms are of the form \r\n" );
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document.write( "\"1%2F%28k%2A%28k%2B1%29%29\" = \"1%2Fk+-+1%2F%28k%2B1%29\"     (if to forget about the common numerator \"15\" for a minute . . . )\r\n" );
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document.write( "the last term is\r\n" );
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document.write( "\"1%2F9900\" = \"1%2F%2899%2A100%29\" \"1%2F99-1%2F100\".\r\n" );
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document.write( "Now, if to sum up all these lines, all internal terms will cancel each other, and the sum will be simply  \"1%2F6+-+1%2F100\".\r\n" );
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document.write( "Now recall about the numerator \"15\" and multiply by 15. You will get your\r\n" );
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document.write( "Answer.  The sum is equal to  \"15%2F6+-+15%2F100\".\r\n" );
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document.write( "         You can simplify it further, if you want.\r\n" );
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