<math>\leq 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\dots</math>
<math>=1++\frac{1}{2}++\frac{1}{2}+\dots</math>
Adding together an infinte string of halves will not give you a finite number so this sequence is said to '''diverge'''.