Algebra.Com's Answer #851331 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "For a positive integer n, let f(n) denote the integer that is closest to sqrt[4]{n}.
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document.write( "Find the integer m so that sum_{n = 1}^m f(n) = 100.
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document.write( " I solved this problem using MS Excel.\r
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document.write( " My calculations are shown in the table below.\r
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document.write( "First column of the table in the counter of natural numbers n = 1, 2, 3, . . . \r\n" );
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document.write( "Second column is the values of  , rounded to the closest integer number.\r\n" );
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document.write( "Third column is the sum S(n) of the first n integer numbers of the second column.\r\n" );
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document.write( "The table shows that the integer 'm' such that the sum S(m) is precisely \r\n" );
document.write( "equal to 100 is 48.\r\n" );
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document.write( "n S(n)\r\n" );
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document.write( "1 1 1\r\n" );
document.write( "2 1 2\r\n" );
document.write( "3 1 3\r\n" );
document.write( "4 1 4\r\n" );
document.write( "5 1 5\r\n" );
document.write( "6 2 7\r\n" );
document.write( "7 2 9\r\n" );
document.write( "8 2 11\r\n" );
document.write( "9 2 13\r\n" );
document.write( "10 2 15\r\n" );
document.write( "11 2 17\r\n" );
document.write( "12 2 19\r\n" );
document.write( "13 2 21\r\n" );
document.write( "14 2 23\r\n" );
document.write( "15 2 25\r\n" );
document.write( "16 2 27\r\n" );
document.write( "17 2 29\r\n" );
document.write( "18 2 31\r\n" );
document.write( "19 2 33\r\n" );
document.write( "20 2 35\r\n" );
document.write( "21 2 37\r\n" );
document.write( "22 2 39\r\n" );
document.write( "23 2 41\r\n" );
document.write( "24 2 43\r\n" );
document.write( "25 2 45\r\n" );
document.write( "26 2 47\r\n" );
document.write( "27 2 49\r\n" );
document.write( "28 2 51\r\n" );
document.write( "29 2 53\r\n" );
document.write( "30 2 55\r\n" );
document.write( "31 2 57\r\n" );
document.write( "32 2 59\r\n" );
document.write( "33 2 61\r\n" );
document.write( "34 2 63\r\n" );
document.write( "35 2 65\r\n" );
document.write( "36 2 67\r\n" );
document.write( "37 2 69\r\n" );
document.write( "38 2 71\r\n" );
document.write( "39 2 73\r\n" );
document.write( "40 3 76\r\n" );
document.write( "41 3 79\r\n" );
document.write( "42 3 82\r\n" );
document.write( "43 3 85\r\n" );
document.write( "44 3 88\r\n" );
document.write( "45 3 91\r\n" );
document.write( "46 3 94\r\n" );
document.write( "47 3 97\r\n" );
document.write( "48 3 100 <<<---===\r\n" );
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document.write( "So, the ANSWER to the problem's question is m = 48.\r\n" );
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document.write( "Having this table, one can construct a wording solution, retelling this my solution in wording form\r\n" );
document.write( "without using this table, but I prefer direct arguments.\r\n" );
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document.write( "Solved.\r
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