document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199973>Question 1199973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear MathTutor, <BR>\n" );
document.write( "I appreciate your response on the question I asked regarding the repeated fractions, however, I have failed to grasp a certain part of it. \r<BR>\n" );
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document.write( "Ref: https://www.algebra.com/tutors/students/your-answer.mpl?question=1199949\r<BR>\n" );
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document.write( "Could you please explain why <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+1+ ALIGN=MIDDLE  ALT=\"+x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > can replace that chunk due to its \"repeated nature\". \r<BR>\n" );
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document.write( "I understand the repeated nature, but not how it justifies this substitution. Please elaborate. Really appreciate it!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833971 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \text{x}-1=\frac{1}{1 + \frac{1}{2+\frac{1}{1+\frac{1}{2+\ldots}}}}\">\r<BR>\n" );
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document.write( "Anywhere we see \"x-1\", we can replace it with that massive nested continued fraction on the right hand side.\r<BR>\n" );
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document.write( "But buried within the continued fraction, is a copy of itself. It's fractal in nature.\r<BR>\n" );
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document.write( "That's how we're able to go from this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1+=+1%2F%281+%2B+1%2F%282%2Bhighlight%281%2F%281+%2B+1%2F%28matrix%281%2C3%2C%222%22%2C%22%2B%22%2C%22...%22%29%29%29%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1+=+1%2F%281+%2B+1%2F%282%2Bhighlight%28%28x-1%29%29%29%29 ALIGN=MIDDLE  ALT=\"x+-+1+=+1%2F%281+%2B+1%2F%282%2Bhighlight%28%28x-1%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The stuff in the red box can be replaced with x-1 since x-1 is equal to that very stuff. \r<BR>\n" );
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document.write( "-----------------------------------\r<BR>\n" );
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document.write( "Another example of this process\r<BR>\n" );
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document.write( "x = sqrt(2+sqrt(2+sqrt(2+...)))<BR>\n" );
document.write( "x = sqrt(2+<font color=red>sqrt(2+sqrt(2+...))</font>)<BR>\n" );
document.write( "x = sqrt(2+<font color=red>x</font>)<BR>\n" );
document.write( "The stuff in red represents x since x is the repeated nested square root.<BR>\n" );
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