Step 1 :Identify the geometric series with first term \(a = \frac{5}{3}\) and common ratio \(r = \frac{5}{3}\)
Step 2 :Use the formula for the nth partial sum of a geometric series: \(S_n = \frac{a(r^n - 1)}{r - 1}\)
Step 3 :Calculate the fourth partial sum (\(S_4\)): \(S_4 = \frac{\frac{5}{3}(\left(\frac{5}{3}\right)^4 - 1)}{\frac{5}{3} - 1}\)