# Cut it the right way

Calculus Level 5

$\large \lim_{n\to\infty} \bigg ( 4^n (3-\sqrt{3+3T_n} ) \bigg )$

Consider the recurrence relation $$T_n = \sqrt{2+T_{n-1}}$$ with $$T_0 = 0$$. If the limit above can be expressed as $$A \pi^B$$ for rational numbers $$A$$ and $$B$$, find the value of $$B\div A$$.

×