1. Prove or disprove: 2. Let denote the distance from x to the nearest integer. What is the value of (Note that this sum can be doubly infinite. For example, when x = 1/3 the terms are nonzero as k...

1. Prove or disprove:

2. Let

denote the distance from x to the nearest integer. What is the value of

(Note that this sum can be doubly infinite. For example, when x = 1/3 the terms are nonzero as k → −∞ and also as k → +∞.)