sum of series

[eturnell]

I am looking at last year's UIL District 1 math test, #45. How do you find the digit in the ten-thousandth place of the sum of a series?

[bradp]

e^x = x^0/0! + x^1/1! + x^2/2! ...
1 - 2 + 2 - 4/3 + 2/3 - 4/15 = (-2)^0/0! + (-2)^1/1! + (-2)^2/2! + (-2)^3/3! ..... = e^-2 = .135335..