The set $\left\{\sum_{n=1}^{\infty} \frac{a_n}{10^n}: a_1=5, a_2=3\right.$, and $a_n \in\{0,1, \ldots, 9\}$ for all $\left.n \geq 3\right\}$ coincides with the set

• A

  $\{x: 0.53 \leq x \lt 0.6\}$
• B

  $\{x: 0.53 \leq x \leq 0.6\}$
• C

  $\{x: 0.53 \leq x \lt 0.54\}$
• Correct answer
  D

  $\{x: 0.53 \leq x \leq 0.54\}$

Hence, the correct answer is option: 'D'.