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avatar+374 

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

 Sep 19, 2024
 #1
avatar+33653 
+1

Find the common ratio, r, given by the ratio of one term divided by the immediately preceeding term.  The infinite series sum is then a/(1-r) where a is the first term.

 Sep 19, 2024
 #2
avatar+1085 
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Evaluate the infinite geometric series  
0.4 + 0.036 + 0.0000324 + ...  

 

0.036 / 0.4                ==>>    ratio = 0.09    

0.0000324 / 0.036    ==>>    ratio = 0.00009    

 

These ratios aren't the same, so that was not a geometric series.   

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 Sep 19, 2024

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