Who can help find the remainder of the Taylor series?

Question

Mathematics

I have a function 1/sqrt(1-x), I expanded it into a Taylor series and now I need to count up to so many n-terms so that the remainder term is just no more than my E (it is equal to 10^(-9)) . How should I do? How to determine to what term to consider the sum of the Taylor series at a = 0?
There is a formula for the remainder, but theta is from 0 to 1, what value should I take? How to count?
en.wikipedia.org/wiki/%D0%A0%D1%8F%D0%B4_%D0%A2%D0...

Answer 1

Take the value of theta at which the absolute value of the remainder term is maximum?