document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=883766>Question 883766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a local species of dragonfly can be found using an infinite geometric series where a1 = 30 and the common ratio is two fifths. Write the sum in sigma notation and calculate the sum that will be the upper limit of this population. \r<BR>\n" );
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document.write( " a)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is 50. \r<BR>\n" );
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document.write( " b)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent. \r<BR>\n" );
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document.write( " c)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is 50. \r<BR>\n" );
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document.write( " d)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent. <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 #533766 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=533766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S = a/(1 - r)\r<BR>\n" );
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document.write( "S = 30/(1 - 2/5)\r<BR>\n" );
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document.write( "S = 50\r<BR>\n" );
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document.write( "So the sum is 50.\r<BR>\n" );
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document.write( "The sigma notation is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{i=1}^{\infty}30\left(\frac{2}{5}\right)^{i-1}\">\r<BR>\n" );
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document.write( "So the answer is <font color=\"red\">choice a)</font>\r<BR>\n" );
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document.write( "<font color=\"red\">a)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is 50. </font><BR>\n" );
document.write( "b)the summation of 30 times two fifths to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.<BR>\n" );
document.write( "c)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is 50.<BR>\n" );
document.write( "d)the summation of two fifths times 30 to the i minus 1 power, from i equals 1 to infinity.; the sum is divergent.  </SPAN>\n" );
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