document.write( "Question 1209977: For a positive integer n, let f(n) denote the integer that is closest to
\n" ); document.write( " $\"root%284%2Cn%29\"$ . Find the integer m so that
\n" ); document.write( " $\"sum%28f%28n%29%2Cn=1%2Cm%29\"$ $\"%22%22=%22%22\"$ $\"100\"$ .
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Algebra.Com's Answer #851333 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "For a positive integer n, let f(n) denote the integer that is closest to\r\n" );
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document.write( "So terms 1 through 5 are all 1's.  That's 5-1+1 = 5 terms of 1's\r\n" );
document.write( "We have 5 terms so far. And so far the sum is 5x1 = 5.\r\n" );
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document.write( "So terms 6 through 39 are all 2's.  That's 39-6+1=34 terms of 2's.\r\n" );
document.write( "We have 5+34=39 terms so far. And so far the sum is 5 + 34x2 = 5 + 68 = 73\r\n" );
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document.write( "So terms from 39 on are all 3's.  So we only need to know how many more terms of\r\n" );
document.write( "3's we need beyond the 39 terms to raise the sum of 73 to 100.\r\n" );
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document.write( "We need to raise the sum by 100-73=27 which will require 27/3=9 more terms of 3's.\r\n" );
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document.write( "So the total number of terms will be 39+9 = 48.\r\n" );
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document.write( "So m = 48\r\n" );
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document.write( "Edwin

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