Find the relation between the 3 wavelengths from energy level diagram

Find E=hc/Lamda for each case.As h and c are constants they cancel out .
So,
Ec-Eb=hc/lamda1
​Eb-Ea=hc/lambda2
​and Ec-Ea=hc/lambda 3
If we add Ec-Eb and Eb-Ea we get Ec-Ea or

Ec-Ea=hc/lamda1+hc/lambda2

or hc/lamda3=hc/lamda1+hc/lamda2
​or 1/lamda3=1/lamda 1+1/lamda2