document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=933035>Question 933035</A>: <I><SPAN STYLE=\"word-break: break-all;\"> prove that 1/n > 1/2power of n by using mathematical induction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566575 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=566575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> True for n = 1\r<BR>\n" );
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document.write( "Assume <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{n} > \frac{1}{2^n}\"> for some fixed <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large n \ge 1\">\r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{2n} > \frac{1}{2^{n+1}}\"> by multiplying both sides by 1/2. However <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{n+1} \ge \frac{1}{2n}\"> since n is at least 1. It follows from transitivity that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \frac{1}{n+1} > \frac{1}{2^{n+1}}\"> so the statement is true for all <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large n \ge 1\">. </SPAN>\n" );
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