document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73789>Question 73789</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132191415/algebrahomeworkh>college algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Im stumped!!! Is there an easy way to do these? Thanks so much!\r<BR>\n" );
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document.write( "Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:<BR>\n" );
document.write( "a) 	What is r, the ratio between 2 consecutive terms? <BR>\n" );
document.write( "Answer:	<BR>\n" );
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document.write( "b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.<BR>\n" );
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document.write( "c)Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.<BR>\n" );
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document.write( "d) 	What observation can make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?<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 #52776 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=52776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Starting with the sequence of: 1, 1/2, 1/4, 1/8,...<BR>\n" );
document.write( "a) Find the common ratio.<BR>\n" );
document.write( "The common ratio, r, is found by dividing any term by the preceeding term.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281%2F2%29%2F1 ALIGN=MIDDLE  ALT=\"r+=+%281%2F2%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1%2F2 ALIGN=MIDDLE  ALT=\"r+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281%2F8%29%2F%281%2F4%29 ALIGN=MIDDLE  ALT=\"r+=+%281%2F8%29%2F%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+%281%2F8%29%2A%284%2F1%29 ALIGN=MIDDLE  ALT=\"r+=+%281%2F8%29%2A%284%2F1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1%2F2 ALIGN=MIDDLE  ALT=\"r+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The common ratio is 1/2\r<BR>\n" );
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document.write( "b) The partial sum of the first n terms of a geometric series is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D+=+%28a%5B1%5D%281-r%5En%29%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D+=+%28a%5B1%5D%281-r%5En%29%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the number of the term (1st, 2nd, 3rd,...)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the common ratio. <BR>\n" );
document.write( "To find the partial sum of the first 10 terms, set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+10 ALIGN=MIDDLE  ALT=\"n+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"a%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1%2F2 ALIGN=MIDDLE  ALT=\"r+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute these values into the formula for the partial sum. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B10%5D+=+%281%281-%281%2F2%29%5E10%29%29%2F%281-%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"S%5B10%5D+=+%281%281-%281%2F2%29%5E10%29%29%2F%281-%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B10%5D+=+0.9990%2F0.5 ALIGN=MIDDLE  ALT=\"S%5B10%5D+=+0.9990%2F0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B10%5D+=+1.9980 ALIGN=MIDDLE  ALT=\"S%5B10%5D+=+1.9980\"   DISABLED_style= \"max-width:90%; height:auto;\" > To four decimal places.<BR>\n" );
document.write( "You should be able to finish the other parts using the above as a guide.<BR>\n" );
document.write( "If you have trouble with it, please re-post.\r<BR>\n" );
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document.write( "c) Find the partial sum of the first 12 terms.<BR>\n" );
document.write( "For this part, n = 12 and we can use the same formula for the partial sum of the first n terms of a geometric sequence.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D+=+%281%281-%281%2F2%29%5E12%29%29%2F%281-1%2F2%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D+=+%281%281-%281%2F2%29%5E12%29%29%2F%281-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D+=+0.9998%2F%281%2F2%29 ALIGN=MIDDLE  ALT=\"S%5B12%5D+=+0.9998%2F%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D+=+1.9995 ALIGN=MIDDLE  ALT=\"S%5B12%5D+=+1.9995\"   DISABLED_style= \"max-width:90%; height:auto;\" > To four deicimal places.\r<BR>\n" );
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document.write( "d) My observation is that the sum approaches 2.<BR>\n" );
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