document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1035624>Question 1035624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose in a proof of the summation formula 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) by mathematical induction, you show the formula valid for n = 1 and assume that it is valid for n = k. What is the next equation in the induction step of this proof?\r<BR>\n" );
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document.write( "1 + 5 + 9 + ... + (4k - 3) = k(2k - 1) + (4(k+1) - 3)<BR>\n" );
document.write( "1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)<BR>\n" );
document.write( "1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (k + 1)[2(k + 1) - 1]<BR>\n" );
document.write( "1 + 5 + 9 + ... + (4k - 3) = k(2k - 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650364 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the second line of the proof...\r<BR>\n" );
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document.write( "1 + 5 + 9 + ... + (4k - 3) + (4(k+1) - 3) = k(2k - 1) + (4(k+1) - 3)\r<BR>\n" );
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document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k%5E2+-+k+%2B+4k+%2B4+-+3+=+2k%5E2+%2B+3k+%2B+1+=+%28k%2B1%29%282k%2B1%29+=+%28k+%2B+1%29%282%28k%2B1%29-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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