document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=287961>Question 287961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm struggling with this one. <BR>\n" );
document.write( "Let f(n)=1^2+2^2+3^2+...+n^2.  <BR>\n" );
document.write( "Thus, <BR>\n" );
document.write( "f(1)=1^2<BR>\n" );
document.write( "f(2)=1^2+2^2<BR>\n" );
document.write( "f(3)=1^2+2^2+3^2<BR>\n" );
document.write( "f(4)=1^2+2^2+3^2+4^2<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "It turns out that f is a polynomial of degree 3 in n.  Figure out the coefficients of f:<BR>\n" );
document.write( "f(n)=__n^3+__n^2+__n+__. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208732 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=208732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm struggling with this one. <BR>\n" );
document.write( "Let f(n)=1^2+2^2+3^2+...+n^2. <BR>\n" );
document.write( "Thus, <BR>\n" );
document.write( "f(1)=1^2<BR>\n" );
document.write( "f(2)=1^2+2^2<BR>\n" );
document.write( "f(3)=1^2+2^2+3^2<BR>\n" );
document.write( "f(4)=1^2+2^2+3^2+4^2<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "It turns out that f is a polynomial of degree 3 in n. Figure out the coefficients of f:<BR>\n" );
document.write( "f(n)=__n^3+__n^2+__n+__.<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Number pairs:<BR>\n" );
document.write( "1::::1<BR>\n" );
document.write( "2::::1+4 = 5<BR>\n" );
document.write( "3::::1+4+9 = 14<BR>\n" );
document.write( "4::::14+16 = 30<BR>\n" );
document.write( "5::::30+25 = 55<BR>\n" );
document.write( "6::::55+36 = 91<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "I ran a Cubic Regression program against <BR>\n" );
document.write( "these pairs and got the following:<BR>\n" );
document.write( "f(n) = (1/3)n^3 + (1/2)n^2 + (833/5000)n^2<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============================================== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );