# What is $$\pi$$ doing here?

Calculus Level 4

$\lim_{n \to \infty} 2^{n+\frac{5}{2}} \sqrt{3-\sqrt{3+3T_{n}}}$

Define a sequence $$T$$ with $$n^\text{th}$$ term $$T_{n}$$ such that $$T_{0} = 0$$ and $$T_{n} = \sqrt{2+T_{n-1}}$$. Then evaluate the limit above.

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