document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177060>Question 1177060</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The closed form sum of\r<BR>\n" );
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document.write( "12 [ 1^2 * 2 + 2^2 * 3 + ... + n^2 (n+1) ]<BR>\n" );
document.write( "for n <= 1 is n(n+1)(n+2)(an+b). Find an + b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805315 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=805315\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Obviously, from the form of the expression, the statement of the problem is supposed to say that the closed form of the sum is for n >=1 -- not for n <= 1.<br><BR>\n" );
document.write( "There are only two unknowns in the problem -- a and b.  So two equations in a and b should be enough to solve the problem.<br><BR>\n" );
document.write( "n=1....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%282%281%5E2%29%29+=+12%282%29+=+24+=+%281%29%282%29%283%29%28a%281%29%2Bb%29+=+6%28a%2Bb%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb+=+4 ALIGN=MIDDLE  ALT=\"a%2Bb+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "n=2....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%282%281%5E2%29%2B3%282%5E2%29%29+=+12%282%2B12%29+=+168+=+%282%29%283%29%284%29%28a%282%29%2Bb%29+=+24%282a%2Bb%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  -->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb+=+7 ALIGN=MIDDLE  ALT=\"2a%2Bb+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a+b=4; 2a+b=7 --> a=3, b=1.<br><BR>\n" );
document.write( "ANSWER: an+b = 3n+1<br><BR>\n" );
document.write( "CHECK for n=3....<br><BR>\n" );
document.write( "12(2(1^)+3(2^2)+4(3^2) = 12(2+12+36) = 600<BR>\n" );
document.write( "(3)(4)(5)(3(3)+1) = 600<br><BR>\n" );
document.write( " </SPAN>\n" );
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