# JEE Type

Geometry Level pending

Let H be the orthocentre of $$\triangle ABC$$ for $$A (0,0)$$,$$B(8,0)$$,$$C (4,4\sqrt { 3 } )$$

If $$G_1, G_2, G_3, \ldots$$ are centroids of triangles $$\triangle AHB, \triangle AG_1 B, \triangle A G_2 B \ldots$$ respectively.

Find the value of $$\displaystyle{\lim _{ n\rightarrow \infty }{ \sum _{ k=1 }^{ n }{ \text{Area}(\Delta A{ G }_{ k }B) } } }$$.

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