■ No GDC ■An empty well is situated at the center of a village. Initially, at time \(t = 0\) minutes, the well contains no coins. At \(t = 1\) minute, a single coin is dropped into the well. At \(t = 2\) minutes, two more coins are dropped into the well; and at \(t = 3\), three more coins are dropped into the well. This process continues until time \(t = n\) minutes.(a) Show that, at time \(t = n\) minutes, there are a...