# Making his way to infinity

Geometry Level 3

An insect starts moving from the origin, $$(0,0)$$ along the straight line in zig-zag manner. He first moves to $$A = (3,3)$$, changes directions and walks half that distance to $$B$$, changes direction and walks a further half of the distance to $$C$$, so on and so forth.

If it ultimately ends at a point $$(a,b)$$, then find the value of $$a+b$$.

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