document.write( "Question 315720: Evaluate the product of the following fractions:
\n" ); document.write( " $\"%28%281%2F2+-1%2F3%29+%2F+%281%2F3-1%2F4%29%29\"$ $\"%22%D7%22\"$ $\"%28%281%2F4+-+1%2F5%29%2F%281%2F5-1%2F6%29%29\"$ $\"%22%D7%22\"$ $\"%28%281%2F6-1%2F7%29%2F%281%2F7-1%2F8%29%29\"$ $\"%22%D7%22\"$ $\"%22%B7%B7%B7%22\"$ $\"%22%D7%22\"$ $\"%28%281%2F98-1%2F99%29%2F%281%2F99-1%2F100%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #225883 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28%281%2F2+-1%2F3%29+%2F+%281%2F3-1%2F4%29%29\"$ $\"%22%D7%22\"$ $\"%28%281%2F4+-+1%2F5%29%2F%281%2F5-1%2F6%29%29\"$ $\"%22%D7%22\"$ $\"%28%281%2F6-1%2F7%29%2F%281%2F7-1%2F8%29%29\"$ $\"%22%D7%22\"$ $\"%22%B7%B7%B7%22\"$ $\"%22%D7%22\"$ $\"%28%281%2F98-1%2F99%29%2F%281%2F99-1%2F100%29%29\"$
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "The sequence of upper left denominators is 2,4,6,8,ЗЗЗ,98, and the\r\n" );
document.write( "general term for those upper left denominators is 2n, where n goes \r\n" );
document.write( "from 1 to 49. \r\n" );
document.write( "\r\n" );
document.write( "Therefore the general factor of the whole product is \r\n" );
document.write( "\r\n" );
document.write( " where n goes from 1 to 49\r\n" );
document.write( "\r\n" );
document.write( "Simplifying this general factor:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( ", where n goes from 1 to 49.\r\n" );
document.write( "\r\n" );
document.write( "Substituting in n=1, \r\n" );
document.write( "Substituting in n=2, \r\n" );
document.write( "Substituting in n=3, \r\n" );
document.write( "ЗЗЗ\r\n" );
document.write( "Substituting in n=47, \r\n" );
document.write( "Substituting in n=48, \r\n" );
document.write( "Substituting in n=49, \r\n" );
document.write( "\r\n" );
document.write( "So we have:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As we see every numerator cancels with the denominator of the next factor,\r\n" );
document.write( "except in the last, or 49th, factor where there is no next factor.  And every\r\n" );
document.write( "denominator gets canceled with the preceding numerator except the 1st factor\r\n" );
document.write( "where there is no preceding factor.  Thus the product becomes:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );