How to get the bounds of exponential function

Question

I have this function $(\frac{d}{d+1})^d$. How can I get the lower and upper bound of this function

Answer 1

$$\frac{1}{2}\geq\left(\frac{d}{d+1}\right)^d=\left(\frac{1}{1+1/d}\right)^d\geq\frac{1}{e}$$