document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1021838>Question 1021838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi im having so much trouble proving this formula with mathematical induction.<BR>\n" );
document.write( "Please help!\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%281%2A3%29%2B1%2F%283%2A5%29 ALIGN=MIDDLE  ALT=\"+1%2F%281%2A3%29%2B1%2F%283%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F%28%282n-1%29%282n%2B1%29%29=n%2F%282n%2B1%29+ ALIGN=MIDDLE  ALT=\"%2B1%2F%28%282n-1%29%282n%2B1%29%29=n%2F%282n%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Basis step: n=1 was true<BR>\n" );
document.write( "Assumption step: n=k <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F%28%282k-1%29%282k%2B1%29%29=k%2F%282k%2B1%29+ ALIGN=MIDDLE  ALT=\"%2B1%2F%28%282k-1%29%282k%2B1%29%29=k%2F%282k%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Induction step: Prove true for n=(k+1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%281%2A3%29%2B1%2F%283%2A5%29 ALIGN=MIDDLE  ALT=\"+1%2F%281%2A3%29%2B1%2F%283%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F%28%282k-1%29%282k%2B1%29%29 ALIGN=MIDDLE  ALT=\"%2B1%2F%28%282k-1%29%282k%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F%28%282%28k%2B1%29-1%29%282%28k%2B1%29%2B1%29%29=%28k%2B1%29%2F%282%28k%2B1%29%2B1%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F%281%2A3%29%2B1%2F%283%2A5%29 ALIGN=MIDDLE  ALT=\"+1%2F%281%2A3%29%2B1%2F%283%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2F%282k%2B1%29+ ALIGN=MIDDLE  ALT=\"k%2F%282k%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B1%2F%28%282k%2B1%29%282k%2B3%29%29=%28k%2B1%29%2F%282k%2B3%29+ ALIGN=MIDDLE  ALT=\"%2B1%2F%28%282k%2B1%29%282k%2B3%29%29=%28k%2B1%29%2F%282k%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "From here I have no idea what to do, to the LHS to make it equal to RHS\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #637534 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=637534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The assumption of induction is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2A3%29%2B+1%2F%283%2A5%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2A3%29%2B+1%2F%283%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282k-1%29%282k%2B1%29%29=k%2F%282k%2B1%29+ ALIGN=MIDDLE  ALT=\"1%2F%28%282k-1%29%282k%2B1%29%29=k%2F%282k%2B1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282k%2B1%29%282k%2B3%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%282k%2B1%29%282k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to BOTH sides.\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2A3%29%2B+1%2F%283%2A5%29 ALIGN=MIDDLE  ALT=\"1%2F%281%2A3%29%2B+1%2F%283%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+...+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%282k-1%29%282k%2B1%29%29%2B1%2F%28%282k%2B1%29%282k%2B3%29%29=k%2F%282k%2B1%29+%2B1%2F%28%282k%2B1%29%282k%2B3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "(Note: 1) The last equation is TRUE by the induction hypothesis. 2) We added 1/(2k+1)(2k+3) because it is supposed to be the next term in line after 1/(2k-1)(2k+1).)\r<BR>\n" );
document.write( "\n" );
document.write( "The RHS of the last equation is equal to \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%282k%2B3%29%29%2F%28%282k%2B1%29%282k%2B3%29%29+%2B+1%2F%28%282k%2B1%29%282k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28k%282k%2B3%29%29%2F%28%282k%2B1%29%282k%2B3%29%29+%2B+1%2F%28%282k%2B1%29%282k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282k%5E2%2B3k%2B1%29%2F%28%282k%2B1%29%282k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%282k%5E2%2B3k%2B1%29%2F%28%282k%2B1%29%282k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282k%2B1%29%28k%2B1%29%29%2F%28%282k%2B1%29%282k%2B3%29%29 ALIGN=MIDDLE  ALT=\"%28%282k%2B1%29%28k%2B1%29%29%2F%28%282k%2B1%29%282k%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2B1%29%2F%282k%2B3%29 ALIGN=MIDDLE  ALT=\"%28k%2B1%29%2F%282k%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I leave the rest of the inductive argument to you... </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );