<s>[INST] The value of \(x\) is calculated using the formula:
\[
x = \alpha + \frac{1}{\alpha+1} + \frac{1}{\text{ breakpoints }} \alpha + \frac{1}{\alpha+1} + ... 
\]
where the series continues indefinitely with the pattern of each subsequent term's denominator being the sum of \(\alpha\) and the previous term's denominator. What value does \(x\) approach as the number of terms increases without bound?[/INST]