Find the sum of the areas of these triangles if this process is continued infinitely.

Question

The hypotenuese of an isosceles right triangle is 17 inches. The midpoints of its sides are connected to form an inscribed triangle, and this process is repeated, creating a third triangle inscribed in the previous one. Find the sum of the areas of these triangles if this process is continued infinitely. 

Answer 1

The process will create an infinite series with terms A_n = (s₁}²(1/2^2n-1) which has the sum (2/3)(s₁)^2.