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<HTML><HEAD><TITLE>Case 3 (#tex2html_wrap_inline68059#)</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="tex2html6414" HREF="page456.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6412" HREF="page452.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6406" HREF="page454.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6416" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H4><A NAME="SECTION0014340300000000000000">Case 3 ( <IMG WIDTH=43 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline68059" SRC="img1802.gif"  >)</A></H4><P>In this case the term  <IMG WIDTH=30 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline68037" SRC="img1794.gif"  > is greater than oneand we make use of the general formula for a finitegeometric series summation (see Section&nbsp;<A HREF="page53.html#secmodelaboutgeometric"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>)to evaluate the summation:<P> <IMG WIDTH=349 HEIGHT=47 ALIGN=BOTTOM ALT="displaymath68057" SRC="img1803.gif"  ><P><P>Substituting this result in Equation&nbsp;<A HREF="page452.html#eqnalgsiii"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> and simplifying gives:<P> <IMG WIDTH=500 HEIGHT=158 ALIGN=BOTTOM ALT="eqnarray32915" SRC="img1804.gif"  ><P><HR><A NAME="tex2html6414" HREF="page456.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6412" HREF="page452.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6406" HREF="page454.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6416" 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 &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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