document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137525>Question 1137525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the infinite geometric series converges. If it does, then find the sum\r<BR>\n" );
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document.write( "(5/4)+(5/16)+(5/64)+... </SPAN>\n" );
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document.write( "We start with 5/4 as the first term<BR>\n" );
document.write( "To get the next term, we multiply by 1/4<BR>\n" );
document.write( "(5/4)*(1/4) = 5/16<BR>\n" );
document.write( "and then multiply that term by 1/4 to get the third term<BR>\n" );
document.write( "(5/16)*(1/4) = 5/64<BR>\n" );
document.write( "and so on\r<BR>\n" );
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document.write( "a = 5/4 is the first term<BR>\n" );
document.write( "r = 1/4 is the common ratio<BR>\n" );
document.write( "Because r = 1/4 = 0.25 is between -1 and 1, this means the infinite geometric series does converge. In other words, that r value makes -1 < r < 1 true.\r<BR>\n" );
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document.write( "So we use the formula below to find the infinite sum S<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2F4%29%2F%281-1%2F4%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2F4%29%2F%281-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2F4%29%2F%284%2F4-1%2F4%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2F4%29%2F%284%2F4-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2F4%29%2F%283%2F4%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2F4%29%2F%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2F4%29%2A%284%2F3%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2F4%29%2A%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2A4%29%2F%284%2A3%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2A4%29%2F%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2Ahighlight%284%29%29%2F%28highlight%284%29%2A3%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2Ahighlight%284%29%29%2F%28highlight%284%29%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%285%2Across%284%29%29%2F%28cross%284%29%2A3%29 ALIGN=MIDDLE  ALT=\"S+=+%285%2Across%284%29%29%2F%28cross%284%29%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+5%2F3 ALIGN=MIDDLE  ALT=\"S+=+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The geometric series converges to the sum of 5/3 = 1.6667</font> </SPAN>\n" );
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