even

1+1/2!+1/4!+1/6!+1/8!+⋯=1.54308084

odd

1+1/3!+1/5!+1/7!+1/9!+⋯=1.17520119

even – odd

1/2!-1/3!+1/4!-1/5!+1/6!-1/7!+⋯=.54308064-.17520119=.36787945

.36787945=1/e