In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?

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In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10?

Base 2 .11111 means:
(1/2)^1 + (1/2)^2 + + (1/2)^3 + (1/2)^4
1/2 + 1/4 + 1/8 + 1/16
This approaches 1