$$ ( \frac { 1 } { 8 } ) + ( \frac { 1 } { 8 } ) ^ { 2 } + ( \frac { 1 } { 1 } ) ^ { 3 } + ( \frac { 1 } { 8 } ) ^ { 4 } + ( \frac { 1 } { 8 } ) ^ { 5 } + \ldots . $$

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To find the sum of the given series, we can use the formula for the sum of an infinite geometric series:

$$ S = \frac{a}{1 - r} $$

where:
- $$ a $$ is the first term of the series
- $$ r $$ is the common ratio of the series

In this case, the first term $$ a = \frac{1}{8} $$ and the common ratio $$ r = \frac{1}{8} $$.

Substitute these values into the formula to find the sum of the series:

$$ S = \frac{\frac{1}{8}}{1 - \frac{1}{8}} $$

Now, let's calculate the sum.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\frac{1}{8}}{\left(1-\frac{1}{8}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{1}{8}}{1-\frac{1}{8}}$$
- step2: Subtract the numbers:
  $$\frac{\frac{1}{8}}{\frac{7}{8}}$$
- step3: Multiply by the reciprocal:
  $$\frac{1}{8}\times \frac{8}{7}$$
- step4: Reduce the numbers:
  $$1\times \frac{1}{7}$$
- step5: Multiply:
  $$\frac{1}{7}$$
The sum of the given series is $$ \frac{1}{7} $$ or approximately 0.142857.
The sum of the series is $$ \frac{1}{7} $$ or approximately 0.142857.

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