document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191490>Question 1191490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the sum:\r<BR>\n" );
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document.write( "1/4(1^3) + 1/9((1^3) + (2^3)) + 1/16((1^3) + (2^3) + (3^3)) +...+ 1/2704((1^3) + (2^3) + (3^3) +...+ (51^3)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823283 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=823283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The fractional part of the n-th term is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28n%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"1%2F%28n%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The other factor in the n-th term is the sum of the cubes of the first n integers:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%282n-1%29%5E3%2C1%2Cn%29=%28%28n%28n%2B1%29%29%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"sum%28%282n-1%29%5E3%2C1%2Cn%29=%28%28n%28n%2B1%29%29%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the nth term in the sequence is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28n%2B1%29%5E2%29%28%28%28n%28n%2B1%29%29%2F2%29%5E2%29=%281%2F%28n%2B1%29%5E2%29%28%28n%5E2%2F4%29%28n%2B1%29%5E2%29+=+n%5E2%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There are 51 terms in the sequence, so the sum is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sum%28n%5E2%2C1%2C51%29%2F4%29 ALIGN=MIDDLE  ALT=\"%28sum%28n%5E2%2C1%2C51%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the formula for the sum of the first n squares to get the final answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%2851%29%2852%29%28103%29%29%2F6%29%2F4=%28%2851%29%2852%29%28103%29%29%2F24=%28%2817%29%2813%29%28103%29%29%2F2=%28%28221%29%28103%29%29%2F2=22763%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 22763/4<br><BR>\n" );
document.write( " </SPAN>\n" );
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