document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198372>Question 198372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the product (1- 1/2)(1- 1/3)(1- 1/4) (1-1/5)…(1-1/99)(1-1/100) is equal to <BR>\n" );
document.write( "a) 1/99  b) 1/80  c) 1/90  d)  1/100   e)  none of these<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148866 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take note that we can combine the terms of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\ldots\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100\right)\">\r<BR>\n" );
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document.write( "to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\left(\frac{4}{5}\right)\ldots\left(\frac{98}{99}\right)\left(\frac{99}{100\right)\">\r<BR>\n" );
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document.write( "Now take note that the second numerator (2) cancels out with the first denominator (2). Likewise, the third numerator (3) cancels out with the second denominator (3). Furthermore, the fourth numerator (4) cancels out with the third denominator (4). This pattern continues on indefinitely. So after these terms cancel out, we're simply left with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{100}\">\r<BR>\n" );
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document.write( "So this means that \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\ldots\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100\right) = \frac{1}{100}\"><BR>\n" );
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