What's the name of the approximation $(1+x)^n \approx 1 + xn$?

Question

A good approximation of $(1+x)^n$ is $1+xn$ when $|x|n << 1$. Does this approximation have a name? Any leads on estimating the error of the approximation?

Answer 1

Wikipedia calls it Binomial Approximation.

Answer 2

I would say it comes from the Bernoulli inequality. You can read it up on Wiki

Answer 3

I would just call it the first order truncation of the Binomial series. If you want more terms of the series, then it's given by $$(1+x)^n = 1 + nx + \frac{n(n-1)}{2}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \mathcal{O}(x^4)$$ for the full series, you can visit the link I provided.

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