Data 605 Week 14 Discussion

Page 475 24. Write out first 5 terms of the Binomial series with given k-value k= 4

Maclaurin Series of f(x): \({\Sigma_{n=0}^\infty\frac{f^{(n)}(0)}{n!}x^n}\)

= \({(1+x)^4}\)

= 1 + k + \({\frac{k(k-1)}{2!}+\frac{k(k-1)(k-2)}{3!}+\frac{k(k-1)(k-2)(k-3)}{4!}}\)

= 1 + 4x + \({6x^2}\) + \({4x^3}\) + \({x^4}\)