document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102037>Question 1102037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show, by	the Principle of Mathematical Induction:	<BR>\n" );
document.write( "8 + 16 + 24+…+8n	= 4n(n+1) for n&#8805;1						 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716664 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Show, by the Principle of Mathematical Induction:	<BR>\n" );
document.write( "8 + 16 + 24+…+8n = 4n(n+1) for n&#8805;1<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Show it is true for n = 1<BR>\n" );
document.write( "8 = 4(2)<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Assume it is true for n = k<BR>\n" );
document.write( "8 + 2*8 + 3*8 + ... + 8k = 4k(k+1)<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Show that it must be true for n = k+1<BR>\n" );
document.write( "8 + 2*8 + 3*8 + ... + 8k + (k+1)8 = 4(k+1)(k+2)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Note:: The 1st 8 terms = 4k(k+1) so you get::<BR>\n" );
document.write( "4k(k+1) + (k+1)(8) = (k+1)[4k+8] = (k+1)*4(k+2) = 4(k+1)(k+2)<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "------------	 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );