document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164006>Question 1164006</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) Simplify<BR>\n" );
document.write( "\[\frac{\binom{n}{k}}{\binom{n}{k - 1}}.\]\r<BR>\n" );
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document.write( "B) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a,b,c that satisfy a:b:c = 1:7:35. What must n be?<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 #788297 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=788297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "part (a)....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck%29+=+%28n%21%29%2F%28%28k%21%29%28n-k%29%21%29 ALIGN=MIDDLE  ALT=\"C%28n%2Ck%29+=+%28n%21%29%2F%28%28k%21%29%28n-k%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck-1%29+=+%28n%21%29%2F%28%28%28k-1%29%21%29%28n-k%2B1%29%21%29 ALIGN=MIDDLE  ALT=\"C%28n%2Ck-1%29+=+%28n%21%29%2F%28%28%28k-1%29%21%29%28n-k%2B1%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck%29%2FC%28n%2Ck-1%29+=+%28%28%28k-1%29%21%29%28n-k%2B1%29%21%29%2F%28%28k%21%29%28n-k%29%21%29+=+%28%28k-1%29%21%2Fk%21%29%2A%28%28n-k%2B1%29%21%2F%28n-k%29%29%21+=+%28n-k%2B1%29%2Fk ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "part (b)....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck%29%2FC%28n%2Ck-1%29+=+%28n-k%2B1%29%2Fk ALIGN=MIDDLE  ALT=\"C%28n%2Ck%29%2FC%28n%2Ck-1%29+=+%28n-k%2B1%29%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck-1%29%2FC%28n%2Ck-2%29+=+%28n-k%29%2F%28k%2B1%29 ALIGN=MIDDLE  ALT=\"C%28n%2Ck-1%29%2FC%28n%2Ck-2%29+=+%28n-k%29%2F%28k%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The problem tells us<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck%29%2FC%28n%2Ck-1%29+=+7%2F1 ALIGN=MIDDLE  ALT=\"C%28n%2Ck%29%2FC%28n%2Ck-1%29+=+7%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28n%2Ck-1%29%2FC%28n%2Ck-2%29+=+35%2F7+=+5%2F1 ALIGN=MIDDLE  ALT=\"C%28n%2Ck-1%29%2FC%28n%2Ck-2%29+=+35%2F7+=+5%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-k%2B1%29%2Fk+=+7 ALIGN=MIDDLE  ALT=\"%28n-k%2B1%29%2Fk+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-k%29%2F%28k%2B1%29+=+5 ALIGN=MIDDLE  ALT=\"%28n-k%29%2F%28k%2B1%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve the pair of equations for k and n:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7k+=+n-k%2B1 ALIGN=MIDDLE  ALT=\"7k+=+n-k%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28k%2B1%29+=+n-k ALIGN=MIDDLE  ALT=\"5%28k%2B1%29+=+n-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8k-n+=+1 ALIGN=MIDDLE  ALT=\"8k-n+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6k-n+=+-5 ALIGN=MIDDLE  ALT=\"6k-n+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k+=+6 ALIGN=MIDDLE  ALT=\"2k+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+3 ALIGN=MIDDLE  ALT=\"k+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+23 ALIGN=MIDDLE  ALT=\"n+=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: n = 23 (and k=3)<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2823%2C3%29%2FC%2823%2C2%29+=+1771%2F253+=+7 ALIGN=MIDDLE  ALT=\"C%2823%2C3%29%2FC%2823%2C2%29+=+1771%2F253+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2823%2C4%29%2FC%2823%2C3%29+=+8855%2F1771+=+5 ALIGN=MIDDLE  ALT=\"C%2823%2C4%29%2FC%2823%2C3%29+=+8855%2F1771+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );