Sum of Infinite Series
To find the sum of the given infinite series, we can start by analyzing the pattern of the terms.

Pattern Analysis
Looking at the given terms 1/6, 5/36, 19/216, 65/1296, 211/7776, we can observe that each term is formed by adding the previous term multiplied by a certain factor. In this case, the factor seems to be increasing by 4 with each term.

General Formula
We can express the nth term of the series as: \( \frac{(6n-5)}{6^n} \)

Summation of Infinite Series
To find the sum of the infinite series, we can use the formula for the sum of an infinite geometric progression:
Sum = \( \frac{a}{1-r} \), where a is the first term and r is the common ratio.
In this case, a = 1/6 and r = 4/6. Substituting these values into the formula, we get:
Sum = \( \frac{\frac{1}{6}}{1-\frac{4}{6}} = \frac{\frac{1}{6}}{\frac{2}{6}} = \frac{1}{2} \)
Therefore, the sum of the infinite series 1/6 + 5/36 + 19/216 + 65/1296 + 211/7776 + ... is 1/2.