The conversation between human and AI assistant.
Z=(1^2) - (2^2) + (3^2) - (4^2) +...- (2998^2) + (2999^2). What is the value of Z?
Interesting. Can you explain how it's used in physics?
Certainly. The potential energy of a system of charged particles can be calculated by adding up the potential energy between each pair of particles. The formula for the potential energy between two particles is kq1q2/r, where k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them. Since the potential energy depends on the distance between particles, the sum can be written as a continuous integral. And if the particles are uniformly distributed in a spherical shell, the integral can be simplified to n(n+2)/3*r^3, where n is the number of particles and r is the radius of the shell. This formula is equivalent to the sum of squares of consecutive odd numbers, with n being the last odd number.