Imagine you are stacking an infinite number of spheres of decreasing radii on top of each other. The radii of the spheres are 1m, 1/2^(1/2)m, 1/3^(1/2)m, etc. . . The spheres are made of a material that weighs 1 newton per cubic meter. . .

1.) How high is the infinite stack of spheres

2.) What is the total surface area of all the spheres in the stack

3.) Show that the weight of the stack is finite.