document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82383>Question 82383</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395430542/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Which series has a sum?<BR>\n" );
document.write( "A. 1-2+4-8+...<BR>\n" );
document.write( "B. 1+3+5+7+...<BR>\n" );
document.write( "C. -1+1-1+1-...<BR>\n" );
document.write( "D. 0.1+0.2+0.3+0.4+...<BR>\n" );
document.write( "E. 0.21+0.0021+0.000021+... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59112 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=59112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 0.21+0.0021+0.000021+...<BR>\n" );
document.write( "This is a repeating decimal so it is a rational number. <BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Adding the terms you would get 0.2121212121....<BR>\n" );
document.write( "Let x= 0.212121212...<BR>\n" );
document.write( "Then 100x = 21.2121212121...<BR>\n" );
document.write( "Subtract the 1st equation from the 2nd to ge:<BR>\n" );
document.write( "99x= 21<BR>\n" );
document.write( "Then x=21/99<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );