document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=26590>Question 26590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let (Tn) = (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . .) be the Fibonacci sequence defined by<BR>\n" );
document.write( "T1 = T2 = 1, Tn = T(n&#8722;1) + T(n&#8722;2) if n > 2.<BR>\n" );
document.write( "Show that the following hold for n that is greator or equal to 1.\r<BR>\n" );
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document.write( "T2+T3+...+T(2n-1)=T(2n) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #14481 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=14481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let (Tn) = (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . .) be the Fibonacci sequence defined by<BR>\n" );
document.write( "T1 = T2 = 1, Tn = T(n&#8722;1) + T(n&#8722;2) if n > 2.<BR>\n" );
document.write( "Show that the following hold for n that is greator or equal to 1. <BR>\n" );
document.write( "T2+T3+...+T(2n-1)=T(2n)<BR>\n" );
document.write( "WE HAVE <BR>\n" );
document.write( "T1=1<BR>\n" );
document.write( "T2=1.......OR.......................................T2-T1=0<BR>\n" );
document.write( "T3=T2+T1............................................T3-T2=T1<BR>\n" );
document.write( "T4=T3+T2............................................T4-T3=T2<BR>\n" );
document.write( "T5=T4+T3............................................T5-T4=T3<BR>\n" );
document.write( "...........................................................................<BR>\n" );
document.write( ".............................................................................<BR>\n" );
document.write( "T2N=T(2N-1)+T(2N-2)...........................T2N-T(2N-1)=T(2N-2)<BR>\n" );
document.write( "ADDING ALL ABOVE ,WE FIND ON THE LHS ,ALL EXCEPT T2N AND -T1 CANCEL EACH OTHER.SO WE GET<BR>\n" );
document.write( "T2N-T1=T1+T2+T3+.........+T(2N-2)...OR......<BR>\n" );
document.write( "T2N=T1+{T1+T2+T3+........T(2N-2)}<BR>\n" );
document.write( "T2N=1+{T1+T2+T3+........T(2N-2)}...THIS IS THE ANSWER.YOUR QUESTION IS NOT CORRECT YOU CAN CHECK AS BELOW...WE HAVE <BR>\n" );
document.write( "T1=1..=	1<BR>\n" );
document.write( "T2=1..=	1<BR>\n" );
document.write( "T3=1+1=	2<BR>\n" );
document.write( "T4=2+1=	3<BR>\n" );
document.write( "T5=3+2=	5<BR>\n" );
document.write( "T6=5+3=	8<BR>\n" );
document.write( "T7=8+5=	13<BR>\n" );
document.write( "T8=13+8=21	..SO T2N=T8=1+T1+T2+T3+T4+T5+T6=1+(1+1+2+3+5+8)=21..THAT IS <BR>\n" );
document.write( ".........................T8=1+{T1+T2+T3+........T(8-2)}...AND NOT<BR>\n" );
document.write( "T2N=T2+T3+...+T(2n-1) WHICH GIVES US T8=T2+T3+T4+T5+T6+T(8-1)<BR>\n" );
document.write( "=1+2+3+5+8+13=32...WHICH IS NOT CORRECT AS T8=21<BR>\n" );
document.write( "FURTHER FIBONACCI SEQUENCE IS <BR>\n" );
document.write( "0,1,1,2,3,5,8......ETC...WITH THE PROPERTY THAT TN=T(N-1)+T(N-2)...AND T1=0 AND T2=1.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );