An object hanging on a spring is pulled downward a distance of 100 cm from its equilibrium position (the origin) and released. It recoils upward past the origin to a height 90 cm above the origin. It continues to oscillate up and down about the origin, but with each oscillation the spring travels only 9/10 of the lass distance traveled. (a) Write an infinite series that models the object's movement. (b) Find the sum of the infinite series. (c) Interpret the sum of the infinite series in the context of the problem.