document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108444>Question 1108444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let Sn = 1+2+4+...+2^n-1.  Find {n: Sn > 1 000 000} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723447 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Note that...<BR>\n" );
document.write( "S1 = 1 = 2-1 = 2^1-1<BR>\n" );
document.write( "S2 = 3 = 4-1 = 2^2-1<BR>\n" );
document.write( "S3 = 7 = 8-1 = 2^3-1<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Sn = ... = 2^n-1<br><BR>\n" );
document.write( "The \"-1\" makes little difference when we get up around a million; so essentially we are looking for the largest value of n for which 2^n is less than 1 million.<br><BR>\n" );
document.write( "2^10 = 1024 which is just a bit more than 1000, so 2^20 will be just a bit more than 1 million.<br><BR>\n" );
document.write( "So the largest n for which the series has a sum of less than 1,000,000 is n=19. </SPAN>\n" );
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