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.

  • $\begingroup$ 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. $\endgroup$ – Shubham Johri Dec 20 '18 at 5:21
  • $\begingroup$ @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. $\endgroup$ – John Omielan Dec 20 '18 at 5:43
  • $\begingroup$ 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 $\endgroup$ – Shubham Johri Dec 20 '18 at 6:00

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