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The Rydberg equation doesn't show different energy levels and how to conceptually get from one level to another one. Thus, it's easy to either get mixed up with emission vs absorption or to just completely forget to concepts behind the formula.
The equation you stated is a derivation of -hr/nfinal^2 - (-hr/ninitial^2). If you factor out the -hr you should get an equation similar to what you posted. As the others stated the equation we learned in class is easier to see conceptually.
We are actually totally allowed to use the Rydberg equation, whereas using the (final - initial) form of the the Rydberg equation could give us a better understanding of the concept and therefore what we are doing. And I believe that using the form of equation recommended by professor Lavelle eliminates the probability of confusing the final state with the initial state.
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