Question 1042593
<pre><b>
{{{(1-1/3) (1-1/4) (1-1/5)*""*""*(1-1/n)}}}{{{""=""}}}

Let's write a couple of terms before the last

{{{(2/3)(3/4)(4/5)*""*""*(1-1/(n-2))(1-1/(n-1))(1-1/n))}}}{{{""=""}}}


{{{(2/3)(3/4)(4/5)*""*""*( ((n-2)-1)/(n-2))( ((n-1)-1)/(n-1) )((n-1)/n)))}}}{{{""=""}}}

{{{(2/3)(3/4)(4/5)*""*""*( (n-2-1)/(n-2))( (n-1-1)/(n-1) )((n-1)/n)}}}{{{""=""}}}

{{{(2/3)(3/4)(4/5)*""*""*( (n-3)/(n-2))( (n-2)/(n-1) )((n-1)/n)}}}{{{""=""}}}

Then start cancelling:

{{{(2/cross(3))(cross(3)/cross(4))(cross(4)/cross(5))*""*""*( cross(n-3)/cross(n-2))( cross(n-2)/cross(n-1) )(cross(n-1)/n)}}}{{{""=""}}}

Everything cancels except the first numerator and the last
denominator:

Answer:  {{{2/n}}}

Edwin</pre></b>