document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550929>Question 550929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Direction: use one of the formulas for special series to find the sum of the series. <BR>\n" );
document.write( "42 <BR>\n" );
document.write( "&#8721; 1<BR>\n" );
document.write( "i=1 <BR>\n" );
document.write( "1. 42 is on top of the symbol, i=1 is on bottom and 1 on right side. <BR>\n" );
document.write( "2. 5 on top, n on right, n=1 on bottom. the answer is 15 but how?<BR>\n" );
document.write( "3. 18 on top, i=1 on bottom, i on right.<BR>\n" );
document.write( "4. 20 on top, k on right, k=1 on bottom<BR>\n" );
document.write( "5. 6 on top, n^2 on right, n=1 on bottom.<BR>\n" );
document.write( "6. 10 on top, i^2 on right, i=1 on bottom<BR>\n" );
document.write( "7. 12 on top, i^2 on right, i=1 on bottom<BR>\n" );
document.write( "8. 35 on top, k^2 on right, k=1 on bottom <BR>\n" );
document.write( "again all these problems are shown in this symbol: &#8721; <BR>\n" );
document.write( "thanks for ur help and happy new year!\r<BR>\n" );
document.write( "\n" );
document.write( "please show ur work with each of the problems so i could understand it. thank you very much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359255 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=359255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "I'll do 4 of them.  You can do the other 4.  They are similar to these.\r\n" );
document.write( "\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "1. 42 is on top of the symbol, i=1 is on bottom and 1 on right side. <BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%281%2Ci=1%2C42%29 ALIGN=MIDDLE  ALT=\"sum%281%2Ci=1%2C42%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 = 42\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "2. 5 on top, n on right, n=1 on bottom. the answer is 15 but how?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28n%2C1=1%2C5%29 ALIGN=MIDDLE  ALT=\"sum%28n%2C1=1%2C5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1+2+3+4+5 = 15 We didn't need a formula but we can use it:\r\n" );
document.write( "              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%285%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"5%285%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%29%286%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28%285%29%286%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 15\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "4. 20 on top, k on right, k=1 on bottom<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28k%2Ck=1%2C20%29 ALIGN=MIDDLE  ALT=\"sum%28k%2Ck=1%2C20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20\r\n" );
document.write( "\r\n" );
document.write( "We use the formula  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2820%2B1%29%2F2 ALIGN=MIDDLE  ALT=\"20%2820%2B1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2820%29%2821%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28%2820%29%2821%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 210\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "8. 35 on top, k^2 on right, k=1 on bottom<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 1>\r\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28k%5E2%2Ci=1%2C35%29 ALIGN=MIDDLE  ALT=\"sum%28k%5E2%2Ci=1%2C35%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1²+2²+3²+4²+5²+6²+7²+8²+9²+10²+11²+12²+13²+14²+15²+16²+17²+18²+19²+20²+21²+22²+23²+24²+25²+26²+27²+28²+29²+30²+31²+32²+33²+34²+35²\r\n" );
document.write( "</font>\r\n" );
document.write( "We use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B1%29%282n%2B1%29%2F6 ALIGN=MIDDLE  ALT=\"n%28n%2B1%29%282n%2B1%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2835%2B1%29%282%2A35%2B1%29%2F6 ALIGN=MIDDLE  ALT=\"35%2835%2B1%29%282%2A35%2B1%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2835%29%2836%29%2870%2B1%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28%2835%29%2836%29%2870%2B1%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2835%29%2836%29%2871%29%29%2F6 ALIGN=MIDDLE  ALT=\"%28%2835%29%2836%29%2871%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 14910.\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );