document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135717>Question 1135717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use mathematical induction to prove the statement is true for all positive integers n. <BR>\n" );
document.write( "6 + 12 + 18 + ... + 6n = 3n(n + 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753368 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "n=1:  (3*1)*(1+1) = 6<BR>\n" );
document.write( "n=2:  (3*2)*(2+1) = 18 = 6 + 12<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Assume true for n=k:  n=k --> Sum = 3k(k+1)<BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Now let n=k+1:\r<BR>\n" );
document.write( "\n" );
document.write( "  Sum = (6+12+18+...+6k) + 6(k+1)<BR>\n" );
document.write( "      = 3k(k+1) + 6(k+1)<BR>\n" );
document.write( "      = 3(k+1)(k+2)    <<<< factored out 3(k+1) from previous line\r<BR>\n" );
document.write( "\n" );
document.write( "This concludes the proof.  <BR>\n" );
document.write( "     \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "        <BR>\n" );
document.write( "          </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );