Discussion 14: APEX Calculus Version - Chapter 4 Exercises 21 -(Page 496)

Problem 21 Chapter 8 (Page 496)

Write out the first 5 terms of the Binomial series with the given k-value: k = 1/2

1. The Term for n=0:

\[\binom{\frac{1}{2}}{0}x^0 = 1\]

2. The Term for n=1:

\[\binom{\frac{1}{2}}{1}x^1 = \frac{1}{2}x\]

3. The Term for n=2:

\[\binom{\frac{1}{2}}{2}x^2 = -\frac{1}{8}x^2\]

4. The Term for n=3:

\[\binom{\frac{1}{2}}{3}x^3 = \frac{1}{16}x^3\]

5. The Term for n=4:

\[\binom{\frac{1}{2}}{4}x^4 = -\frac{5}{128}x^4\]

So, the first 5 terms of the binomial series are as follows:

\(==> 1 + \frac{1}{2}x -\frac{1}{8}x^2 \frac{1}{16}x^3 -\frac{5}{128}x^4 ...\)