document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121014>Question 1121014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1/15+1/35+1/63+1/99+1/143/+1/199=<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736744 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=736744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I suspect the last fraction is typed incorrectly.  1/195 would make a much nicer problem.  I will solve the problem using 1/195 instead of 1/199.<br><BR>\n" );
document.write( "The series can be written as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%283%2A5%29%2B1%2F%285%2A7%29%2B1%2F%287%2A9%29%2B1%2F%289%2A11%29%2B1%2F%2811%2A13%29%2B1%2F%2813%2A15%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Each term can be written in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28n-1%29%28n%2B1%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28n-1%29%28n%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Decomposing that fraction shows each term can be written in the form <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%281%2F%28n-1%29-1%2F%28n%2B1%29%29%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%28%281%2F%28n-1%29-1%2F%28n%2B1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the sum is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%28%281%2F3-1%2F5%29%2B%281%2F5-1%2F7%29%2B%281%2F7-1%2F9%29%2B%281%2F9-1%2F11%29%2B%281%2F11-1%2F13%29%2B%281%2F13-1%2F15%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%281%2F3-1%2F15%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%281%2F3-1%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%284%2F15%29+=+2%2F15 ALIGN=MIDDLE  ALT=\"%281%2F2%29%284%2F15%29+=+2%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If the last fraction is really 1/199, then treat that last fraction separately; the sum will be<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%281%2F3-1%2F13%29%2B1%2F199 ALIGN=MIDDLE  ALT=\"%281%2F2%29%281%2F3-1%2F13%29%2B1%2F199\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );