document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=837300>Question 837300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have this sum:<BR>\n" );
document.write( "1 + 4 + 12 + 32 + ... + 2^(n-1)*n<BR>\n" );
document.write( "I haven't done calculus in a while so I can't remember how to do it<BR>\n" );
document.write( "( 2^(n-1)*n = 2 to the power of (n-1), everything times n )\r<BR>\n" );
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document.write( "Cheers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #504573 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=504573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Break up the sum as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \sum_{k=1}^{n} 2^{k-1}k = \sum_{k=1}^n 2^{k-1} + \sum_{k=2}^{n} 2^{k-1} + \ldots + \sum_{k = n}^n 2^{k-1}\">\r<BR>\n" );
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document.write( "Each of the summations on the RHS is a geometric series, which can be evaluated with some algebra. </SPAN>\n" );
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