document.write( "Question 1210233: Show that the sum of n terms of the progression \r
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Algebra.Com's Answer #851710 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Show that the sum of the end term of the progression Log x, Log x^2, Log x^3, log x^4 = n (n+1/2) Log x
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\n" ); document.write( "\n" ); document.write( "        Wording and writing in the post are incorrect, so I edited it to make sense from nonsense.\r
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\n" ); document.write( "\n" ); document.write( "        My edited formulation is as follows:\r
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\n" ); document.write( "\n" ); document.write( "                Show that the sum of n terms of the progression log(x), log(x^2), log(x^3), log(x^4) , . . , log(x^n) is (n*(n+1)/2)*log x.\r
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\n" ); document.write( "\n" ); document.write( "        Below is my solution for this edited formulation.\r
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document.write( "In this problem, x > 0.\r\n" );
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document.write( "Let a = log(x).\r\n" );
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document.write( "Then  = 2a,   = 3a, . . . and so on . . . till   = n*a.\r\n" );
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document.write( "Therefore, our progression takes the form\r\n" );
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document.write( "    a + 2a + 3a + . . . + n*a = (1 + 2 + 3 + . . . + n)*a.\r\n" );
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document.write( "The sum in parentheses in the right side is well known sum of the arithmetic progression,\r\n" );
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document.write( "and it is equal to  .\r\n" );
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document.write( "Thus   +  +  + . . . +  = .\r\n" );
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document.write( "It is the final answer, and the proof is complete.\r\n" );
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