Find the sum of the series $\sum_{i=0}^{\infty}\left(\frac{2}{5}\right)^{i}$, if possible.

Step 1 ：Given the infinite geometric series \(\sum_{i=0}^{\infty}\left(\frac{2}{5}\right)^{i}\)

Step 2 ：The first term a = 1 (when i = 0) and the common ratio r = 2/5

Step 3 ：The sum of an infinite geometric series can be found using the formula S = a / (1 - r), if the absolute value of r is less than 1

Step 4 ：In this case, |r| = 2/5 < 1, so we can use the formula to find the sum

Step 5 ：Substitute a = 1 and r = 0.4 into the formula, we get S = 1 / (1 - 0.4)

Step 6 ：Calculate the expression, we get S = 1.6666666666666667

Step 7 ：Final Answer: The sum of the series is \(\boxed{1.6666666666666667}\)