What is the closed form expression for the sum: Σx2/n! from 0 to N?

[aaaa202]

Is there a closed form expression for the sum:

Σx²/n! from 0 to N

for N=∞ it is an exponential but what about the finite case?

 

[Buzz Bloom]

for N=∞ it is an exponential but what about the finite case?

Hi aaaa202:

The finite sum is a polynomial expression. According to some definitions of "close form" a polynomial is closed. I am pretty sure there is no simpler representational, as there is for the infinite sum.

BTW: You have a typo in the equation:

Σx²/n! from 0 to N

The exponent should be "n", not "2".

Good luck.

Regards,
Buzz