document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=565266>Question 565266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that nCr is less than or equal to n+1Cr+1\r<BR>\n" );
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document.write( ". Hint: Make use of the fact that if A &#8804; B then A/B &#8804;1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365741 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=365741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pascal's triangle easily proves it, as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE nCr + nC(r+1) = (n+1)C(r+1)\">\r<BR>\n" );
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document.write( "Since nC(r+1) is nonnegative, nCr <= (n+1)C(r+1).\r<BR>\n" );
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document.write( "Or, we can show that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{nCr}{(n+1)C(r+1)} \le 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\frac{n!}{(n-r)!r!}}{\frac{(n+1)!}{(n-r)!(r+1)!}} \le 1\">\r<BR>\n" );
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document.write( "Multiply both numerator and denominator by 1/(denominator)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{n!(r+1)!}{(n+1)!r!} \le 1 \Rightarrow n!(r+1)! \le (n+1)!r!\">\r<BR>\n" );
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document.write( "Divide both sides by n!r!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r+1 \le n+1 \Rightarrow r \le n\">\r<BR>\n" );
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document.write( "This is true because we're choosing r objects out of n, so it is reasonable to assume r <= n. </SPAN>\n" );
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