How could the accuracy of a binomial expansion be more accurate?
What values of x is the expansion of (1 + bx)^n valid for?
Where n is negative or a fraction, x is valid for: | bx | < 1 or | x | < 1/b
What values of x is the expansion of (a + x)(1 + bx)^n valid for?
Still | bx | < 1 or | x | < 1/b , ignore first bracket as it’s not to the power of anything
What values of x is the expansion of (1 + x/b)^n valid for?
x/b | < 1, so | x | < b
What values of x is the expansion of a(1 + b/ax)^n valid for?
a/bx | < 1, so | x | < b/a