all of these things are going to be one this is one this is one when we're taking about e^x so you go to the third term this is one you just have x^3 / 3! plus x^3 / 3! and I think you see the pattern here we just keep adding terms x^4 / 4! plus x^5 / 5! plus x^6 over 6! and something pretty neat is starting to emerge this is just really cool that e^x can be approximated by 1 plus x plus x^2 / 2! plus x^3 / 3! once again, e^x is starting to look like a pretty cool thing this also leads to other interesting results