document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353951>Question 353951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using mathematical induction to prove 8+10+12+...+(2n+6) = n^2 +7n , the Pk + 1 statement is 8+10+12+...+(2n+6) = (k+1)+7(k+1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253005 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=253005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using mathematical induction to prove <BR>\n" );
document.write( "8+10+12+...+(2n+6) = n^2 +7n , <BR>\n" );
document.write( "------<BR>\n" );
document.write( "Check for n=1<BR>\n" );
document.write( "8 = 1^2+7*1<BR>\n" );
document.write( "8 = 8<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Assume the formula is true for n = k<BR>\n" );
document.write( "8+10+12+...+(2k+6) = k^2+7k<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Prove the formula is true for n = k+1<BR>\n" );
document.write( "[8+10+12+...+(2k+6)]+(2(k+1)+6) = [k^2+7k] + (2(k+1)+6<BR>\n" );
document.write( "= k^2+7k+2k+8<BR>\n" );
document.write( "= k^2+2k+1+7k+7<BR>\n" );
document.write( "= (k+1)^2+7(k+1)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Therefore the formula is true for all positive whole numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );