Initially 1 square in top row and three squares in second row making four squares = 2^2

Then five squares(2*3-1) in 3rd row are added giving nine sqaures = 3^2

Then seven squares (2*4-1) in 4th row are added giving sixteen squares = 4^2

In the bottom nth row there will be (2n-1) squares. At that time previous n-1 rows will have (n-1)^2

(n-1)^2+2n-1 = n^2-2n+1-2n-1=n^2.

Thus if there are (n-1)^2 in previous figure there will be n^2 squares in next figure. Thus it is true in general.

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