arithmetic - Why is $left(1-frac{1}{k}right)^t < e^{-t/k}$?

I came across this statement, but can't see why it holds: $\left(1-\frac{1}{k}\right)^t < e^{-t/k}$

I'm sure it's something simple, but I don't have a great deal of mathematical experience. I have tried using $e^k = \sum_{n=0}^\infty \frac{\lambda^n}{n!}$, but without success.

Help would be appreciated. Thanks!