<s>[INST] Find the sum of the series $\frac{1}{3}+\frac{1}{4}.\frac{1}{2!}+\frac{1}{5}.\frac{1}{3!}+\cdots$ 
Find the sum of the series $$\frac{1}{3}+\frac{1}{4}.\frac{1}{2!}+\frac{1}{5}.\frac{1}{3!}+\cdots$$

I found that the n-th term of the series is $\frac{1}{n+2}.\frac{1}{n!}$ , but I am unable to find the sum.
 [/INST] HINT:
$$\frac{1}{(n+2)n!}=\frac{1}{(n+1)!}-\frac{1}{(n+2)!}$$
Now telescope.
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