document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=954448>Question 954448</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1+5+14+30+55........<BR>\n" );
document.write( "Find sum to n terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #582926 by </B><A HREF=/tutors/aboutme.mpl?userid=hemu_da><B>hemu_da(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=hemu_da><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=hemu_da><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=582926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is the series of sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms..\r<BR>\n" );
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document.write( "We know that....\r<BR>\n" );
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document.write( "Sum of first n term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%2F4 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum of the square of the first n term is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%282n%2B1%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%282n%2B1%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum of the cube of the first n numbers is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2%28n%2B1%29%5E2%29%2F2 ALIGN=MIDDLE  ALT=\"%28n%5E2%28n%2B1%29%5E2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Given that..\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B5%2B14%2B30%2B55%2B......... ALIGN=MIDDLE  ALT=\"1%2B5%2B14%2B30%2B55%2B.........\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2%2B%281%5E2%2B2%5E2%29%2B%281%5E2%2B2%5E2%2B3%5E2%29%2B%281%5E2%2B2%5E2%2B3%5E2%2B4%5E2%29%2B...... ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%282n%2B1%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%282n%2B1%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "We can write this series also as--- sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28%28n%28n%2B1%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29 ALIGN=MIDDLE  ALT=\"sum%28%28%28n%28n%2B1%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28%28%28n%5E2%2Bn%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29 ALIGN=MIDDLE  ALT=\"sum%28%28%28%28n%5E2%2Bn%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28%282n%5E3%2B3n%5E3%2Bn%29%2F6%29%2Cn=1%2Cn%29 ALIGN=MIDDLE  ALT=\"sum%28%28%282n%5E3%2B3n%5E3%2Bn%29%2F6%29%2Cn=1%2Cn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28%28%28n%5E3%29%2F3%29%2B%28%28n%5E2%29%2F2%29%2B%28n%2F6%29%29%2Cn=1%2Cn%29 ALIGN=MIDDLE  ALT=\"sum%28%28%28%28n%5E3%29%2F3%29%2B%28%28n%5E2%29%2F2%29%2B%28n%2F6%29%29%2Cn=1%2Cn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29sum%28n%5E3%2Cn=1%2Cn%29+%2B+%281%2F2%29sum%28n%5E2%2Cn=1%2Cn%29+%2B+%281%2F6%29sum%28n%2Cn=1%2Cn%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "Sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28%28n%5E2%28n%2B1%29%5E2%29%2F4%29+%2B+%281%2F2%29%28%28n%28n%2B1%29%282n%2B1%29%29%2F6%29+%2B+%281%2F6%29%28%28n%28n%2B1%29%29%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%28n%28n%2B1%29%2B%282n%2B1%29%2B1%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%28n%28n%2B1%29%2B%282n%2B1%29%2B1%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%28n%5E2%2B3n%2B2%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%28n%5E2%2B3n%2B2%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ".\r<BR>\n" );
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document.write( "Sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%28n%2B1%29%28n%2B2%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%28n%2B1%29%28n%2B2%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sum= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%28n%2B1%29%5E2%28n%2B2%29%29%2F12 ALIGN=MIDDLE  ALT=\"%28n%28n%2B1%29%5E2%28n%2B2%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... Ans..\r<BR>\n" );
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document.write( "To varify this formula lets take n=4... <BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%284%2B1%29%5E2%284%2B2%29%29%2F12 ALIGN=MIDDLE  ALT=\"%284%284%2B1%29%5E2%284%2B2%29%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Sum=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2A25%2A6%29%2F12 ALIGN=MIDDLE  ALT=\"%284%2A25%2A6%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Sum= 50.<BR>\n" );
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document.write( "In the series...  Sum of first 4 terms= 1+5+14+30 = 50..<BR>\n" );
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document.write( "Which is equal to the our calculated Ans....<BR>\n" );
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