document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198628>Question 1198628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the convergent series, 5 -10/3 +20/9 -40/27... what does the series converge to?\r<BR>\n" );
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document.write( "The answer is one of the following. Which one?\r<BR>\n" );
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document.write( "A) the series converges to 5\r<BR>\n" );
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document.write( "B) the series converges to 15\r<BR>\n" );
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document.write( "C) the series converges to 3\r<BR>\n" );
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document.write( "D) the series converges to 9 </SPAN>\n" );
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document.write( "Answer: <font color=red>3   (choice C)</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Refer to this previous similar question.<BR>\n" );
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document.write( "In it I discuss that this sequence is geometric with<BR>\n" );
document.write( "a = 5 = first term<BR>\n" );
document.write( "r = -2/3 = common ratio\r<BR>\n" );
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document.write( "I then further explained that<BR>\n" );
document.write( "S = a/(1-r)<BR>\n" );
document.write( "S = 5/(1-(-2/3))<BR>\n" );
document.write( "S = 3<BR>\n" );
document.write( "represents the summation of the infinitely many terms.\r<BR>\n" );
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document.write( "The formula<BR>\n" );
document.write( "S = a/(1-r)<BR>\n" );
document.write( "only works when -1 < r < 1 is true.<BR>\n" );
document.write( "Otherwise, the geometric series would diverge.\r<BR>\n" );
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document.write( "Luckily -1 < -2/3 < 1 is true, so -1 < r < 1 is true for r = -2/3.<BR>\n" );
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