Fundamental frequency is given by

$n=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$

$n \propto \frac{1}{l}(\because T \text { and } \mu \text { are constants })$

Here, $l_{1}=\frac{k}{n_{1}}, l_{2}=\frac{k}{n_{2}}, l_{3}=\frac{k}{n_{3}}$ and $l=\frac{k}{n}$

But $l=l_{1}+l_{2}+l_{3}$

$\therefore \quad \frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}$