How Do Series Expansions Relate to Exponential Functions?

[e^(i Pi)+1=0]

limit as n→∞ of $\frac{(2t)^n}{n!}$ and $\frac{(-t)^n}{n!}$

Answers are e^2t-1 and e^-t-1 but I don't know how to work them out, thanks.

edit: btw these are series

 

[Dick]

If those are series you should fix up your question showing the limits of the series. Do you know $e^a=\Sigma^\infty_0 \frac{a^n}{n!}$?

 

[haruspex]

limit as n→∞ of $\frac{(2t)^n}{n!}$ and $\frac{(-t)^n}{n!}$

Answers are e^2t-1 and e^-t-1 but I don't know how to work them out, thanks.

edit: btw these are series

Starting at n=1, it would seem? That would be unusual.

 

[HallsofIvy]

These are easy if you know that
$$\sum_{n=0}^\infty \frac{x^n}{n!}= e^x$$