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Evaluate the infinite geometric series: ​3/2 + 2/3 + 8/27 + 32/243 + ...

 May 1, 2021
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First, find the common ratio: (2/3)/(3/2) = 4/9

 

Second, factor the infinite geometric series: (3/2)*((4/9)^0 + (4/9)^1 + (4/9)^2 + (4/9)^3 + ... )

 

Third, use the formula 1/(1-x) to solve for ((4/9)^0 + (4/9)^1 + (4/9)^2 + (4/9)^3 + ... ), where x = 4/9:  1/(1-4/9) = 9/5

 

Lastly, simplify: (3/2)*(9/5) = 27/10 or 2.7

 May 2, 2021

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