document.write( "Question 1197721: Find the sum of the series: 18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260. \n" ); document.write( "

Algebra.Com's Answer #831104 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "Find the sum of the series: 18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260.
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\n" ); document.write( "\n" ); document.write( " Step by step\r
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document.write( "(1)  18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260 = 18*(1/12 + 1/20 + 1/30 + 1/42 + . . . + 1/1260).\r\n" );
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document.write( "(2)  Every addend in the parentheses is \r\n" );
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document.write( "      =  =  - \r\n" );
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document.write( "      =  =  - \r\n" );
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document.write( "      =  =  - \r\n" );
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document.write( "      =  =  - \r\n" );
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document.write( "          . . . . . . . . . . . . . . . . \r\n" );
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document.write( "      =  =  - \r\n" );
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document.write( "(3)  Add fractions in n.2, on the left sides and on the right sides.\r\n" );
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document.write( "     On the left side, you will get the sum, which is in parentheses in n.1.\r\n" );
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document.write( "     On the right side, all interior term will cancel each other, and only two extreme terms will survive\r\n" );
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document.write( "        1/12 + 1/20 + 1/30 + 1/42 + . . . + 1/1260 =  -  =  = .\r\n" );
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document.write( "(4)  THEREFORE\r\n" );
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document.write( "        18/12 + 18/20 + 18/30 + 18/42 + ... + 18/1260 =  = .\r\n" );
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document.write( "ANSWER.  The requested sum is equal to  = 5 = 5.5.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a Sunday's school Math circle problem.\r
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