Integral Sequence

Calculus Level 4

Define a sequence of functions \(\{f_n(x)\}\) as follows: \[f_1(x) = 1, \hspace{.4cm} f_{n+1}(x) = \int_0^{\infty}\frac{e^{-tx}}{f_n(t)}dt.\] Evaluate: \[\frac{f_{20}(1)f_{21}(1)}{f_{18}(1)f_{19}(1)}\]

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