I know that the sum of the reciprocals of factorials to infinity and beyond is e by using a Taylor Series for e^x, (1+1/1+1/2+1/6+1/24+...=e), but is there a specific formula for just finding them up to a given n?
1+1/1+1/2+1/6+1/24+...+1/100!
Just curious.
after a very small number of terms, the Lagrange remainder grows so small that the difference from e is negligible...
But is there an explicit function with an exact value? The sum 1/0! up to 1/100! is just e minus the exact error 1/101!+1/102!+...
e^x is a pretty special function, you'd think there'd be something.
I know that the sum of the reciprocals of factorials to infinity and beyond is e by using a Taylor Series for e^x, (1+1/1+1/2+1/6+1/24+...=e), but is there a specific formula for just finding them up to a given n?
1+1/1+1/2+1/6+1/24+...+1/100!
Just curious.