How to approximate 1/3 by only add/subtracting powers of 2 How approximate $\frac{1}{3}$ up to four significant digits by using only $\pm2^n$ where $n$ is a negative integer.
Preliminary attempt/example:
$$0.33\approx0.25+0.0625=0.3125$$
$$=2^{-2}+2^{-4}$$

Following on from where you left off, the sequence $$2^{-2}+2^{-4}+2^{-6}+...$$ converges to $\frac 13$ using the formula for a geometric series
