Prove that the duration of a perpetual bond is given by $\frac{1+r}{r}.$ Hint:

Differentiate equation: ${\displaystyle \underset{n=0}{\overset{}{}}}{q}^n=\frac{1}{1-q}$ w$.$r$.$t$.q.$ You do not need to

prove that you can go with the derivative within the infinite sum.