find the sum sum((cos (frac(n m)/(3^n)))(3^n))

To find the sum \( \sum \left(\frac{\cos \left(\frac{n m}{3^{n}}\right)}{}\right) \), we need to evaluate the expression for each term in the series and then add them up.Let's consider the general term in the series: \( \frac{\cos \left(\frac{n m}{3^{n}}\right)}{} \).The cosine function oscillates between -1 and 1. Therefore, the maximum value of \( \cos \left(\frac{n m}{3^{n}}\right) \) is 1, and the minimum value is -1.To find the sum, we need to consider the behavior of the cosine function as increases. As becomes large, the argument of the cosine function approaches 0. This is because the denominator grows much faster than the numerator .As the argument of the cosine function approaches 0, the cosine function approaches 1. Therefore, the general term \( \frac{\cos \left(\frac{n m}{3^{n}}\right)}{} \) approaches 1 as becomes large.Hence, the sum \( \sum \left(\frac{\cos \left(\frac{n m}{3^{n}}\right)}{}\right) \) approaches as becomes large.