=_[x][0] [n*(1 - (x² / 3!) + (x⁴ / 5!) - (x⁶ / 7!).....inf terms)]

put x = 0

 you will get [n] by putting x = 0 only when the terms would have been finite

but in this case since the terms are infinite hence all the terms after 1 although tend to zero(remember they only tend to zero and do not become equal to zero)   but due to infinite terms thier sum will not be zero.

I hope i made myself clear enough

do as if any doubt