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Find the sum of the infinite series 2/1 + 1/3 + 2/9 + 1/27 + 2/81 + 1/243 + ...

 Dec 9, 2019
 #1
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∑ -1/2 3^(1 - n) ((-1)^n - 3), n, 1, ∞ =21 / 8

 Dec 9, 2019
 #2
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Note that we can split this  as

 

2/1  +  2/9   +  2/81   +   .....+         and

 

1/3  +  1/27   +  1/243  + .... +

 

The  sum of the first series  =         2/  [ 1 - 1/9]  

 

The sum of the second series  =     (1/3)  / [ 1 - 1/9 ] 

 

So.....the sum  =    [ 2 +1/3]  / [ 1 - 1/9]   =   [ 7/3 ] / [ 8/ 9 ] =        63/ 24    =   21 / 8

 

 

 

cool cool cool

 Dec 9, 2019

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