# 4 non-zero terms of Taylor series to approximate

I need to use the first 4 non zero terms binomial Taylor series:

$$(1+x)^r = \sum^{\infty}_{n=0} {(r n)x^n}$$ centered at $$0$$

I need to use this series to approximate $$(1.2)^{1/4}$$ and find the error of this approximation.

I understand that $$r = \frac{1}{4}$$ and $$x = 0.2$$, but i am not sure how to proceed with that information.

What exactly is the question asking me to do? This topic is new to me so I am not sure how to start this problem.

• You just have to approximate the value by finding the first $4$ non-zero terms of the infinite series and adding them up. The error will be given by the next $(5^{th})$ non-zero term of the infinite series. – Shubham Johri Dec 20 '18 at 5:21
• @Shubham Johri, note that, technically, the error of the approximation would be the sum of the remaining terms, i.e., from the next ($5^{th}$) non-zero term on. – John Omielan Dec 20 '18 at 5:43
• It isn't possible to calculate that infinite sum in this and the general case. Depending upon the desired accuracy, we truncate the error term – Shubham Johri Dec 20 '18 at 6:00