Recurring Styles #2 - Recurrence on Higher Degrees!

Calculus Level 5

anan1=an1an226\Large{\frac{a_n}{a_{n-1}} = \sqrt[6]{\frac{a_{n-1}}{a^2_{n-2}}}}

Define a sequence ana_n that satisfies the recurrence relation as described above where n2,a0=e,a1=e2n \geq 2 , a_0 = e , a_1 = e^2.

Find the value of limnan\displaystyle\large{ \lim_{n \to \infty} a_n}.

Bonus: Generalize for ana_n.

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