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, $8! = 1\times2\times3\times\cdots\times8$ .