A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is

Question:

A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is then placed on the first one. This process is continued until n chambers, including the sphere, are formed. (The figure shows the case n = 4.) Use mathematical induction to prove that the maximum height of any bubble tower with n chambers is 1 + √n.

FIGURE FOR PROBLEM 26