Show that the first few frequencies of light that are emitted when electrons falls to the nth level form levels higher than n, are approximate harmonics (i.e., in the ratio 1 : 2: 3...) when `n gt gt 1`.

Explanation

To show that the first few frequencies of light emitted when electrons fall to the nth level from levels higher than n are approximate harmonics (i.e., in the ratio 1:2:3...) when \( n \gg 1 \), we can follow these steps:

### Step 1: Understand the Transition
When an electron transitions from a higher energy level \( m \) to a lower energy level \( n \), it emits a photon with a frequency \( \nu \). According to the Bohr model of the atom, the frequency of the emitted light can be expressed using the Rydberg formula.

### Step 2: Write the Rydberg Formula for Frequency
The formula for the frequency of light emitted during the transition from level \( m \) to level \( n \) is given by:
\[
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