document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093613>Question 1093613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me with this? Thank you. <BR>\n" );
document.write( "I need to prove a series by the principal of mathematical induction. <BR>\n" );
document.write( "sigma sign (up=n, down=(k=0))2^k=2^(n+1)-1<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 #708271 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=708271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sigma sign (up=n, down=(k=0))2^n =2^(n+1)-1<BR>\n" );
document.write( "1st:: Show it is true for k = 0<BR>\n" );
document.write( "2^0 = 2^(0+1)-1<BR>\n" );
document.write( "1 = 2*1-1<BR>\n" );
document.write( "1 = 1<BR>\n" );
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document.write( "2nd:: Assume it is true for n = k::<BR>\n" );
document.write( "2^k = 2^(k+1)-1<BR>\n" );
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document.write( "3rd:: Show that it is true for n = k+1::<BR>\n" );
document.write( "2^(k+1) = 2*2^k = 2[2^(k+1)-1] = 2^(k+2)-2 = 2^[(k+1)+1]-2<BR>\n" );
document.write( "Note:: It is not true in general::<BR>\n" );
document.write( "E.G.:: not true for n = 1<BR>\n" );
document.write( "2^1 = 2^(1+1)-1<BR>\n" );
document.write( "2 = 2^2-1<BR>\n" );
document.write( "2 = 3 <BR>\n" );
document.write( "Is not true<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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