document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187230>Question 187230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i find the sum of this series? 25 is on top of the &#8721; symbol i=1 with (4i+1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140342 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=140342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \sum_{i=1}^{25}(4i + 1)\">\r<BR>\n" );
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document.write( "This means to replace <i>i</i> in 4<i>i</i> + 1 with the integers from 1 to 25 and add up the results.  So the first term is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4(1) + 1 = 5\">\r<BR>\n" );
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document.write( "and the second term is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4(2) + 1 = 9\">\r<BR>\n" );
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document.write( "and so on until you get to the last term which is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4(25) + 1 = 101\">\r<BR>\n" );
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document.write( "Now you could do this the hard way, namely directly compute the sum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5 + 9 ... 97 + 101\">\r<BR>\n" );
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document.write( "But that method is long, arduous, and prone to error.  Fortunately, there is a formula for the sum of any series of numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^n\, \alpha_i\ =\ \frac{(a + l)n}{2}\">\r<BR>\n" );
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document.write( "Where <i>a</i> is the first element of the series, <i>l</i> is the last element of the series, and <i>n</i> is the number of elements.  So for your problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \sum_{i=1}^{25}(4i + 1) =\ \frac{(5 + 101)25}{2}\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.\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" );
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