document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675285>Question 675285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression (1 - 1/2)(1 - 1/3)(1 - 1/4)... ... ... ... (1 - 1/n), where n is a positive integer.\r<BR>\n" );
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document.write( "I have no idea where to begin with this. Could you please help me??<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419785 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=419785\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can write this as<BR>\n" );
document.write( "( 1/2 )*( 2/3 )*( 3/4 )*( 4/5 )* . . . ( n-2)/( n-1 )*( n-1 )/( n )<BR>\n" );
document.write( "There are cancellations on the top and bottom<BR>\n" );
document.write( "I can rewrite the whole thing as<BR>\n" );
document.write( "(2/2)*(3/3)*4/4)* . . . (n-1)/(n-1) * (1/n)<BR>\n" );
document.write( "This equals 1/n<BR>\n" );
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document.write( "You can test it for n = 5, for instance<BR>\n" );
document.write( "( 1/2)*(2/3)*(3/4)*(4/5) = <BR>\n" );
document.write( "(2/2)*(3/3)*(4/4)*(1/5) = 1/5\r<BR>\n" );
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