1. The problem asks to evaluate the sum \( \sum_{i=1}^{\infty} \frac{1}{2i} \). 2. This is an infinite series where each term is \( \frac{1}{2i} \) starting from \( i=1 \) to infinity. 3. We can factor out the constant \( \frac{1}{2} \) from the sum: $$ \sum_{i=1}^{\infty} \frac{1}{2i} = \frac{1}{2} \sum_{i=1}^{\infty} \frac{1}{i} $$ 4. The series \( \sum_{i=1}^{\infty} \frac{1}{i} \) is the harmonic series, which is known to diverge (it grows without bound). 5. Therefore, the original series also diverges and does not have a finite sum. Final answer: The series \( \sum_{i=1}^{\infty} \frac{1}{2i} \) diverges and does not converge to a finite value.