document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112934>Question 112934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find a general term a sub n for the sequence 1/3, 2/4, 3/5, 4/6,... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82266 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=82266\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Looking at the sequence of the numerators, we see: 1,2,3,4,...\r<BR>\n" );
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document.write( "And we can see that the numerators are increasing by 1 each time and start at 1. So if we start at n=0, then the general sequence for the numerators is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at the sequence of the denominators, we see: 3,4,5,6,...\r<BR>\n" );
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document.write( "And we can see that the denominators are increasing by 1 each time, but are starting at 3. So if we start at n=0, then the general sequence for the denominators is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B3 ALIGN=MIDDLE  ALT=\"n%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So putting this all together we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%2F%28n%2B3%29 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%2F%28n%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we let n=0, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B1%29%2F%280%2B3%29=1%2F3 ALIGN=MIDDLE  ALT=\"%280%2B1%29%2F%280%2B3%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we let n=1, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B1%29%2F%281%2B3%29=2%2F4 ALIGN=MIDDLE  ALT=\"%281%2B1%29%2F%281%2B3%29=2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we let n=2, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B1%29%2F%282%2B3%29=3%2F5 ALIGN=MIDDLE  ALT=\"%282%2B1%29%2F%282%2B3%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And finally, if we let n=3, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B1%29%2F%283%2B3%29=4%2F6 ALIGN=MIDDLE  ALT=\"%283%2B1%29%2F%283%2B3%29=4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this verifies our answer. </SPAN>\n" );
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