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document.write( "Here is a geometric series:\r\n" );
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document.write( "2 + 6 + 18 + 54 + 162 + 486\r\n" );
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document.write( "A. It has 6 terms. So we say 
\r\n" );
document.write( "B. It has first term 2. So we say 
\r\n" );
document.write( "C. It has common ratio 3. So we say 
\r\n" );
document.write( "D. It has sum 728. So we say 
\r\n" );
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document.write( "The reason we say it has common ratio 3 is because:\r\n" );
document.write( "1. The 2nd term 6 divided by the 1st term 2 is 3. \r\n" );
document.write( "2. The 3rd term 18 divided by the 2nd term 6 is 3.\r\n" );
document.write( "3. The 4th term 54 divided by the 3rd term 18 is 3. \r\n" );
document.write( "4. The 5th term 162 divided by the 4th term 54 is 3.\r\n" );
document.write( "5. The 6th term 486 divided by the 5th term 162 is 3.\r\n" );
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document.write( "Since all those divisions come out 3, it is a geometric\r\n" );
document.write( "series, with common ratio 3.\r\n" );
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document.write( "The formula for the sum 
of any FINITE geometric series is:\r\n" );
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document.write( "
\r\n" );
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document.write( "So in the above case, substituting:\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "We can also find just by adding:\r\n" );
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document.write( " 2\r\n" );
document.write( " 6\r\n" );
document.write( " 18\r\n" );
document.write( " 54 \r\n" );
document.write( "162 \r\n" );
document.write( "486\r\n" );
document.write( "728\r\n" );
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document.write( "But if there were 100 terms instead of just 6 that would\r\n" );
document.write( "take too long, but the formula would be much shorter.\r\n" );
document.write( "-----------------------------------\r\n" );
document.write( "There are also INFINITE geometric series that never end, but goes\r\n" );
document.write( "on forever and ever. That is when r < 1, like this:\r\n" );
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document.write( "
\r\n" );
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document.write( "A. It has infinitely many terms terms. \r\n" );
document.write( "B. It has first term 8. So we say 
\r\n" );
document.write( "C. It has common ratio 
. So we say 
\r\n" );
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document.write( "We could never add them all up since the terms go on forever.\r\n" );
document.write( "However there is a number that we get closer and closer to as \r\n" );
document.write( "we add more and more terms.\r\n" );
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document.write( "So we say that the sum of all \"infinity\" of those terms is given by\r\n" );
document.write( "this formula:\r\n" );
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document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
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document.write( "
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document.write( "\r\n" );
document.write( "
\r\n" );
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document.write( "
\r\n" );
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document.write( "
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document.write( "So the more terms we add, the closer to 28/3 we will get.\r\n" );
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document.write( "28/3 is the decimal 9.333333333...\r\n" );
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document.write( "Notice that when we add just the first 4 terms we get 9.329446064\r\n" );
document.write( "which is well on the way to 9.333333333...\r\n" );
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document.write( "Hope this helps you.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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document.write( " \n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
