Pulling a long molecule

Suppose that a long molecule is modeled by a one-dimensional string of beads with alternating charges \(+q,-q,+q \ldots \). The distance between the beads is d and its known that \[ F_{0}= \frac{1}{4\pi \epsilon_{0}} \frac{q^{2}}{d^{2}}=10 \textrm{N}.\] One end of the of the string is being pulled by a force (parallel to the molecule) that is slowly increasing with time. What is the maximum force \( F_{max}\) in Newtons so that the molecule does not break.

Details and assumptions

• The following identity may be useful: \[ \sum_{n=1}^{\infty} (-1)^{n-1} \frac{1}{n^{2}}=\frac{\pi^{2}}{12}.\]
• Don't assume you know a priori between which bead the molecule breaks...