document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6221>Question 6221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that the sum of the first N even natural numbers is equal to (1+1/N) times the sum of the first N odd natural numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3926 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=3926\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  You posted this question in wrong category.\r<BR>\n" );
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document.write( " The first N even natural numbers <BR>\n" );
document.write( " Se= 2+ 4+...+ 2n =2(1+2+3+..+n) = 2* n(n+1)/2 = n(n+1)\r<BR>\n" );
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document.write( " The sum of the first N odd natural numbers<BR>\n" );
document.write( " So= 1+3 +...+ (2n-1) [ arthemic series with common difference 2 ]<BR>\n" );
document.write( " = n(1+2n-1)/2 = n^2.<BR>\n" );
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document.write( " We see that (1+ 1/n)So = (1+ 1/n)n^2 = n^2 + n = n(n+1) =Se\r<BR>\n" );
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document.write( " This completes the proof.\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "  </SPAN>\n" );
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