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1⋅21!+2!+2⋅32!+3!+3⋅43!+4!+4⋅54!+5!+⋯= ?\large\dfrac{1\cdot2}{1!+2!}+\dfrac{2\cdot3}{2!+3!}+\dfrac{3\cdot4}{3!+4!}+\dfrac{4\cdot5}{4!+5!}+\cdots=\ ?1!+2!1⋅2+2!+3!2⋅3+3!+4!3⋅4+4!+5!4⋅5+⋯= ?
Notation: !!! denotes the factorial notation. For example, 8!=1×2×3×⋯×88! = 1\times2\times3\times\cdots\times8 8!=1×2×3×⋯×8.
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