Find the sum of the infinite geometric series. 2- 2/3+ 2/9 -2/27+...

Marimaf asked Jul 12, 2022

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26 votes

Find the sum of the infinite geometric series.
2- 2/3+ 2/9 -2/27+...

Marimaf asked Jul 12, 2022

2.5k points

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16 votes

Answer:

3/2

Explanation:

$2-(2)/(3) +(2)/(9) -(2)/(27) +...\\r=(-(2)/(3) )/(2) =-(1)/(3) ,|r|<1\\s_(\infty)=(a)/(1-r) \\=(2)/(1+(1)/(3) ) \\=(2)/((4)/(3) )\\ =(3)/(2)$

Tyrique answered Jul 18, 2022

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