Find the sum of the sequence:

1. \(\frac 1 3 + \frac 1 9\)

2. \(\frac 2 3 + \frac 2 9\)

3. \(\frac 1 3 + \frac 1 9 + \frac{1}{27}\)

4. \(\frac 2 3 + \frac 2 9 + \frac{2}{27}\)

5. \(\frac 1 3 + \frac 1 9 + \frac{1}{27} + \frac{1}{81}\)

6. \(\frac 2 3 + \frac 2 9 + \frac{2}{27} + \frac{2}{81}\)

Priya is walking down a long hallway. She walks halfway and stops. Then, she walks half of the remaining distance and stops again. She continues to stop every time she goes half of the remaining distance.

1. What fraction of the length of the hallway will Priya have covered after she starts and stops 2 times?
2. What fraction of the length of the hallway will Priya have covered after she starts and stops 4 times?
3. Will Priya ever reach the end of the hallway, repeatedly starting and stopping at half the remaining distance? Explain your thinking.