smc

This series is a geometric series with common ratio $\frac{1}{2}$. Using the well-known formula for the sum of an infinite geometric series, we obtain that this series has a value of $2\cdot \frac{1}{1-\frac{1}{2}}=4$. It immediately follows that statements 1 and 2 are false while statements 4 and 5 are true. 3 is false because we cannot make any term of the sequence approach 0, though we can choose some term that is less than any given positive quantity. The correct answer is therefore $\boxed{\text{Only }4\text{ and }5}$.