Determine whether the infinite series converges

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Determine whether the infinite series

5 - 2.5 + 1.25 - 0.625 + \frac{5}{16} - \frac{5}{32} + \frac{5}{64} - \frac{5}{128} + \text{⋯}

converges. Give a brief reason for your answer.