document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=894440>Question 894440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i) give a recursive definition of the set P of all positive integers greater than 0<BR>\n" );
document.write( " II) formulate tha appropriate induction principle<BR>\n" );
document.write( " III) use mathematical induction to prove that<BR>\n" );
document.write( " 11+15+19 +... + (4n+7) = 2n^2 + 9n for all positive n>0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #542050 by </B><A HREF=/tutors/aboutme.mpl?userid=jibirajeev><B>jibirajeev(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jibirajeev><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=542050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My definition p(n)=p(n-1)+1\r<BR>\n" );
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document.write( "11+15+19..+(4n+7)+(4(n+1)+7)=2(n+1)^2+9(n+1)<BR>\n" );
document.write( " =2(n^2+2n+1)+9n+1<BR>\n" );
document.write( " = 2n^2+9n + 4n+2+9<BR>\n" );
document.write( "  =2n^2+9n + 4n+11<BR>\n" );
document.write( "Therefore works for the step up case <BR>\n" );
document.write( "= 4(n+1)+7=4n+11 </SPAN>\n" );
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