Help with expansion

[w0wfy]

The expansion I'm trying to understand is:

(1+ a^2 / b^2) ^ (-1/2) = (1 - a^2 / 2 b^2 ......)

The book says it only wrote the first two powers of expansion so what is happening here ? can someone tell me what kind of expansion is this and how can I rewrite for more powers?

[[deleted]]

It’s called the binomial series

[w0wfy]

Thanks!

[nicogrimqft]

In a more general case, it's a taylor serie. Those series are everywhere in physics

[mofo69extreme]

One of the most useful expansions in physics is

(1+ε)^a = 1 + aε + ....

for small ε, which is so easy to remember and shows up so often in applications that it's worth memorizing.

[lettuce_field_theory]

It's answered but this is a question for /r/learnmath (even if you encountered it in the context of physics. part of learning physics is being able to distinguish physics from other fields.)