document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81942>Question 81942</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;\"> a. write 0.75 as an infinite geometric series. (bar is over 75)<BR>\n" );
document.write( "             <BR>\n" );
document.write( "b. express 0.75 as a fraction in lowest terms by finding the sum of the series.<BR>\n" );
document.write( "(bar is over 75) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58773 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=58773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the decimal repeats, we can break up the series as\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.75+0.0075+0.000075...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this represents a sequence. Notice the first term is 0.75, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=0.75 ALIGN=MIDDLE  ALT=\"a%5B1%5D=0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The common ratio (the constant factor) is then simply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=0.0075%2F0.75=1%2F100 ALIGN=MIDDLE  ALT=\"r=0.0075%2F0.75=1%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So altogether we have the sequence\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=0.75%281%2F100%29%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=0.75%281%2F100%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=%283%2F4%29%281%2F100%29%5En ALIGN=MIDDLE  ALT=\"a%5Bn%5D=%283%2F4%29%281%2F100%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice if n=0 we get our first term 0.75, if n=1, we get 0.0075 etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the series is simply:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28+%283%2F4%29%281%2F100%29%5Ei%2C+i=0%2C+infinity+%29 ALIGN=MIDDLE  ALT=\"sum%28+%283%2F4%29%281%2F100%29%5Ei%2C+i=0%2C+infinity+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );