document.write( "Question 71383This question is from textbook Advanced Algebra
\n" ); document.write( ": Find the sum of the infinite geometric series 3+2+4/3+8/9+..... \n" ); document.write( "

Algebra.Com's Answer #51055 by jim_thompson5910(35256) $\"\"$ $\"About$

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First we need to find the nth term of the series, or in other words the general formula. To go from 3 to 2, multiply by 2/3, and to go from 2 to 4/3 again you must multiply by 2/3. So the geometric ratio r is 2/3 and since the sequence starts at 3, the initial term a=3. So using the infinite sum formula we get
\n" ); document.write( " $\"S=a%2F%281-r%29\"$ Note: r<0 for an infinite sum to converge
\n" ); document.write( " $\"S=3%2F%281-2%2F3%29\"$
\n" ); document.write( " $\"S=3%2F1%2F3\"$
\n" ); document.write( " $\"S=9\"$
\n" ); document.write( "So as the sum of the infinite series is 9. \n" ); document.write( "

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