document.write( "Question 1186901: If S = (log 1/2) + (log 2/3) + (log 3/4) + ... + (log 998/999) + (log 999/1000), where the base of the logarithm is 10, what is the integral value of S in simplest form? \n" ); document.write( "

Algebra.Com's Answer #817866 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "If S = (log 1/2) + (log 2/3) + (log 3/4) + ... + (log 998/999) + (log 999/1000),\r\n" );
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document.write( "then  S = .\r\n" );
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document.write( "Now, in the global product, cancel the denominators and numerators in all neighbor fractions, and you will get simple expression\r\n" );
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document.write( "    S =  = -3.\r\n" );
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document.write( "THEREFORE, the final   A N S W E R   is  S = -3.\r\n" );
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