Sum

50/81 as a fraction. 

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

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