Which geometric series converges, and to what sum?
1+2+4+...1 + 2 + 4 + ... 1+2+4+... converges to 222
1+1+1+...1 + 1 + 1 + ...1+1+1+... converges to 111
12+14+18+...\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...21+41+81+... converges to 111
3+3+3+...3 + 3 + 3 + ...3+3+3+... converges to 333