document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251892>Question 251892</A>: <I><SPAN STYLE=\"word-break: break-all;\">  The sum of the integers from 1 to n is n(n+1) over 2. The sum of the squares of the integers from 1 through n is n(n+1)(2n+1) over 6 . The sum of the cubes of the integers from 1 through n is n^2(n+1)^2 over 4 . Use the appropriate expressions to find the following values. \r<BR>\n" );
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document.write( "B. The sum of the squares from 1 through 30.<BR>\n" );
document.write( "C. The sum of the cubes of the integers from 1 through 30.<BR>\n" );
document.write( "D. The square of the sum of the integers from 1 through 30.<BR>\n" );
document.write( "e. The cube of the sum of the integers from 1 through 30. \r<BR>\n" );
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document.write( "my answers<BR>\n" );
document.write( "B. 620.16<BR>\n" );
document.write( "c.216,225<BR>\n" );
document.write( "D. not really sure how to get started<BR>\n" );
document.write( "e. not really sure how to get started </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183605 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Don't know where you went wrong with part B, but if you think about it for a second, you know that the answer cannot have a decimal fraction.  You are adding a series of integers, and the integers are closed for addition.  That means any time you add two integers, you get another integer.\r<BR>\n" );
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document.write( "Part B:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{n(n\,+\,1)(2n\,+\,1)}{6}\ =\ \frac{30\,\cdot\,31\,\cdot\,61}{6}\">\r<BR>\n" );
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document.write( "Try that arithmetic one more time.\r<BR>\n" );
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document.write( "Part C:\r<BR>\n" );
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document.write( "You have the correct answer.\r<BR>\n" );
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document.write( "Part D and E\r<BR>\n" );
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document.write( "First calculate the sum of the integers from 1 to 30:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{n(n\,+\,1)}{2}\ = \frac{30\,\cdot\,31}{2}\">\r<BR>\n" );
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document.write( "Square the result for part D and cube the result for part E.\r<BR>\n" );
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document.write( "That is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ D = \left(\frac{30\,\cdot\,31}{2}\right)^2\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ E = \left(\frac{30\,\cdot\,31}{2}\right)^3\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
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