# A mathematical journey

Calculus Level 4

${ a }_{ n+1 }=2n{ a }_{ n }$ The recurrence relation above has the initial condition of $$a_1=1$$. Suppose we define the function $S\left( x \right) =\sum _{ n=1 }^{ \infty }{ \frac { { x }^{ n } }{ { a }_{ n } } }.$ Find the value of $$\displaystyle \int _{ 0 }^{ 2 }{ S\left( x \right) \, dx }$$.

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