An unending sequence of points!

Geometry Level 4

\(A_i\) (where \(i \in \left\{ 1,2,3,4, \cdots ,n \right\}\) ) are \(n\) points in a plane whose coordinates are denoted by \(\left( x_i , y_i \right)\) respectively.

  • \(A_1 A_2\) is divided in the ration of \(1:1\) at \(G_1\)
  • \(G_1 A_3\) is divided in the ratio of \(1:2\) at \(G_2\)
  • \(G_2 A_4\) is divided in the ratio of \(1:3\) at \(G_3\)
  • This process continues until
  • \(G_{n-1} A_{k_n}\) is divided in the ratio \(1:n\) at \(G_n\)

What are the coordiantes of \( G_n \)?

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