These Numerators Diverge Too

Algebra Level 3

True or False?

\[ \dfrac1{0!} + \dfrac1{1!} + \dfrac1{2!} + \dfrac1{3!} + \dfrac1{4!} + \cdots = \dfrac0{0!} + \dfrac1{1!} + \dfrac2{2!} + \dfrac3{3!} + \dfrac4{4!} + \cdots \]

\[\] Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).

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