document.write( "Question 1020545: Please help me solve this question.\r
\n" ); document.write( "\n" ); document.write( "Find the value of n:(1-1/2)(2-2/3)(3-3/4)(4-4/5)...(15-15/16)=n!/16 \n" ); document.write( "

Algebra.Com's Answer #636450 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%281-1%2F2%29%282-2%2F3%29%283-3%2F4%29\"$ ... $\"%2814-14%2F15%29%2815-15%2F16%29\"$
\n" ); document.write( "Notice that the kth factor of this expression also has k as a factor,e.g., the factor 3-3/4 has 3 as a factor,and the 14th factor 14-14/15 has 14 as a factor.
\n" ); document.write( "If we factor all the k factors from each one of those factors, the expression becomes\r
\n" ); document.write( "\n" ); document.write( " $\"1%2A2%2A3%2A4\"$ ... $\"13%2A14%2A15%281-1%2F2%29%281-1%2F3%29%281-1%2F4%29\"$ ... $\"%281-1%2F15%29%281-1%2F16%29\"$
\n" ); document.write( "This expression is the same as
\n" ); document.write( " $\"15%21%281%2F2%29%282%2F3%29%283%2F4%29\"$ ... $\"%2814%2F15%29%2815%2F16%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The product of the fifteen fractional terms would just be equal to 1/16 by direct cancellation of common terms.
\n" ); document.write( "Hence the entire expression is equal to \r
\n" ); document.write( "\n" ); document.write( " $\"15%21%281%2F16%29\"$ , \r
\n" ); document.write( "\n" ); document.write( "and so the value of n is $\"highlight%2815%29\"$ . \n" ); document.write( "

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