Circles Meeting a Fixed Line
Difficulty: Medium · Topics: Geometry, Circles, Telescoping
O‘zgarmas to‘g‘ri chiziqni kesuvchi aylanalar
Let x n be the x-coordinate of the point where the circle x^2+y^2=n meets the line y=√3x in the first quadrant. Find
Σ k=1^80frac1x k+x k+1.
x n — x^2+y^2=n aylananing birinchi chorakda y=√3x to‘g‘ri chiziq bilan kesishish nuqtasining x koordinatasi bo‘lsin. Toping:
Σ k=1^80frac1x k+x k+1.