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<HTML><HEAD><TITLE>Case 1 (#tex2html_wrap_inline68035#)</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html6392" HREF="page454.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6390" HREF="page452.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6384" HREF="page452.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6394" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H4><A NAME="SECTION0014340100000000000000">Case 1 ( <IMG WIDTH=43 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline68035" SRC="img1793.gif" >)</A></H4><P>In this case, the term <IMG WIDTH=30 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline68037" SRC="img1794.gif" > falls between zero and one.Consider the <em>infinite</em> geometric series summation:<P> <IMG WIDTH=336 HEIGHT=47 ALIGN=BOTTOM ALT="displaymath68031" SRC="img1795.gif" ><P>Since the infinite series summation approaches a finite constant <I>C</I>and since each term in the series is positive,the <em>finite</em> series summation in Equation <A HREF="page452.html#eqnalgsiii"><IMG ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>is bounded from above by <I>C</I>:<P> <IMG WIDTH=302 HEIGHT=47 ALIGN=BOTTOM ALT="displaymath68032" SRC="img1796.gif" ><P><P>Substituting this result into Equation <A HREF="page452.html#eqnalgsiii"><IMG ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>and making use of the fact that <IMG WIDTH=49 HEIGHT=11 ALIGN=BOTTOM ALT="tex2html_wrap_inline68021" SRC="img1787.gif" >,and therefore <IMG WIDTH=74 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline68045" SRC="img1797.gif" >, gives<P> <IMG WIDTH=500 HEIGHT=112 ALIGN=BOTTOM ALT="eqnarray32892" SRC="img1798.gif" ><P><HR><A NAME="tex2html6392" HREF="page454.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6390" HREF="page452.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6384" HREF="page452.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6394" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright © 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.</ADDRESS></BODY></HTML>⌨️ 快捷键说明
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