Let a sequence of integers  $a_1,a_2,a_3,\mathrm{.......}$ be defined by $a_1=1,a_2=2,a_3=3,a_4=7,a_5=\mathrm{43......}$ and in general  $a_{n+1}=1+a_1\cdot a_2\cdot a_3\mathrm{...}{a}_n\forall n\ge 1$.
If $S_n=\frac{1}{a_1}+\frac{1}{a_2}+\frac{1}{a_3}+\mathrm{....}+\frac{1}{a_n}$  and $P_n=\frac{1}{a_1\cdot a_2\cdot a_3\mathrm{...}{a}_n}$, then the value of $S_{2024}+P_{2024}$ is ___