document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199960>Question 1199960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum k = 0 to 2009 i ^ k </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833976 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13334)</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=833976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "sum k = 0 to 3 (i^k) = 1 + i - 1 - i = 0<br><BR>\n" );
document.write( "Every four consecutive integer powers of i have a sum of 0.<br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "sum k = 0 to 2007 = 0<br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "sum k = 0 to 2009 = 0 + i^2008 + i^2009 = 0 + 1 + i = 1 + i<br><BR>\n" );
document.write( "ANSWER: 1 + i </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );