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Evaluate the sum 1/3 + 2/3^2 + 1/3^3 + 2/3^4 + ...

 May 1, 2022
 #1
avatar+168 
+1

50/81 as a fraction. 

 May 1, 2022
 #2
avatar
+1

∑[ 1/(3^(2*n-1)) +2/(3^(2*n)), n, 1, ∞]==converges to 5/8

 May 1, 2022
 #3
avatar+124595 
+1

1/3 + 2/3^2  + 1/3^3 + 2/3^4 + 1/3^5 + 2/3^6  + 1/ 3^7 + 2/3^8 .........

 

We can write this as

 

(3 + 2)/3^2   + (3 + 2)/3^4  + (3 + 2) / 3^6  + (3 + 2) / 3^8   .....   =

 

5 [  1/3^2  + 1/3^4  +  1/ 3^6  + 1/3^8  .....  ]    =

 

5 [ the sum of an infinite series  with  the first term = 1/3^2  and a  common ratio of 1/3^2 ]  = 

 

5 (1/3^2)  / ( 1 - 1/3^2)  =

 

(5/9) / ( 8/9)  =  

 

5 /  8

 

 

cool cool cool

 May 1, 2022

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