How come? Summation, identity?

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    Identity Summation
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The discussion centers on the approximation e-Δ2/δ2 ≈ 1-Δ2/δ2 when Δ is significantly smaller than δ. This approximation arises from the Taylor expansion of the exponential function, specifically e^x = 1 + x + x²/2! + ..., where lower order terms dominate as x approaches zero. The key takeaway is that for small values of Δ relative to δ, the exponential function can be simplified effectively using its Taylor series expansion.

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How does e22 ≈ 1-Δ22

When Δ<<δ ?

I'm sure it's a basic summation I'm unaware of.
 
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This comes from the Taylor expansion of the exponential function. Remember that
e^x = 1 + x + \frac{x^2}{2!} + \cdots = \sum_{i=0}^\infty \frac{x^i}{i!}
As x gets very small, the lower order terms dominate (since the others go to zero), and so we can approximate the exponential function by taking the first few terms of the Taylor expansion.
 
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