If `x_(n)=cospi/3^(n)+isin(pi)/(3^(n))`, then `x_(1),x_(2),x_(3),………………..x_(infty)` is equal to

Explanation

To solve the problem, we need to evaluate the infinite series defined by \( x_n = \cos\left(\frac{\pi}{3^n}\right) + i \sin\left(\frac{\pi}{3^n}\right) \) for \( n = 1, 2, 3, \ldots \) and find the limit as \( n \) approaches infinity.

### Step-by-Step Solution:

1. **Express \( x_n \) in Exponential Form**:
\[ x_n = \cos\left(\frac{\pi}{3^n}\right) + i \sin\left(\frac{\pi}{3^n}\right) = e^{i \frac{\pi}{3^n}} \]
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