I need help with a summation formula

Question

anonymous · Answer

$$\sum_{n=0}^{\infty} x^n/n! = e^x$$
I know this is so, but I need help understanding why.  I would appreciate it if someone could explain this or point me in the right direction.  Thanks.

myininaya · Answer

cant you just use taylor series to show e^x is that

myininaya · Answer

hey math teacher :)

mathteacher1729 · Answer

This is a bit difficult to explain over open study math. I can set up a twiddla or mathim chat for all the full details, but basically you know that e^x is its own derivative, and that e^0 = 1.  From there, you assume there is some infinite polynomial with constant coefficients which is exactly e^x.  Then differentiate and equate coefficients.

myininaya · Answer

did you ever see my solution to that cal problem i gave us

mathteacher1729 · Answer

Myiniana -- yes, I saw your solution to the limit problem, nicely done. :) (I replied in chat)

Banjo -- if you'd like to go over this in detail, let me know.

anonymous · Answer

I think I understand what you are saying.  I will have to look at it myself a little bit.  I'll let you know if I need more explanation.  Thank you.