>(1/2) + (1/4) + (1/8) + (1/16) + ...
>Does this equal 1 or approach 1?

There's a common definition of a series. An expression like the above represents a number, if convergent. It represents nothing, if divergent. In any event, it does not move anywhere to be able to approach anything. Therefore, according to the common definition, to say that 1/2 + 1/4 + 1/8 + 1/16 + ... approaches 1 would be entirely wrong. On the other hand, the sequence of partial sums

1/2, 1/2 + 1/4, 1/2 + 1/4 + 1/8, 1/2 + 1/4 + 1/8 + 1/16, ...

can be said to approach 1, the number to which 1/2 + 1/4 + 1/8 + 1/16 + ... is equal.