Inspired by Ikkyu San

Calculus Level 4

1231!+2!+3!+2342!+3!+4!+3453!+4!+5!+=?\large\dfrac { 1\cdot 2\cdot 3 }{ 1!+2!+3! } +\dfrac { 2\cdot 3\cdot 4 }{ 2!+3!+4! } +\dfrac { 3\cdot 4\cdot 5 }{ 3!+4!+5! }+\cdots = \, ?

Notation:
!! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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