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 \(l=l_{1}+l_{2}+l_{3}\)

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