document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758998>Question 758998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find sum of infinite series 1/2^n <BR>\n" );
document.write( "and series -1/2^n </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461947 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The nth term of a geometric series is normally written <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_n+=+a%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a_n+=+a%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For this series, we know that the infinite sum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S+=+a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a=1 and r=1/2. This series has terms 1/2, 1/4, 1/8...<BR>\n" );
document.write( "The series above has terms 1, 1/2, 1/4, 1/8...<BR>\n" );
document.write( "So the two series differ by 1.<BR>\n" );
document.write( "The sum of the series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_n+=+%281%2F2%29%5E%28n-1%29+=+1%2F%281-%281%2F2%29%29+=+2 ALIGN=MIDDLE  ALT=\"a_n+=+%281%2F2%29%5E%28n-1%29+=+1%2F%281-%281%2F2%29%29+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore the sum of the series <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a_n+=+%281%2F2%29%5En+=+2-1+=+1 ALIGN=MIDDLE  ALT=\"a_n+=+%281%2F2%29%5En+=+2-1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll leave it to you to figure out the other one. </SPAN>\n" );
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