Integral Sequence

Calculus Level 4

Define a sequence of functions {fn(x)}\{f_n(x)\} as follows: f1(x)=1,fn+1(x)=0etxfn(t)dt.f_1(x) = 1, \hspace{.4cm} f_{n+1}(x) = \int_0^{\infty}\frac{e^{-tx}}{f_n(t)}dt. Evaluate: f20(1)f21(1)f18(1)f19(1)\frac{f_{20}(1)f_{21}(1)}{f_{18}(1)f_{19}(1)}

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