discussion 14

Exercise 8.8.23

Write out the first 5 terms of the Binomial series with the given k-value.

k=1/3

Solution:

1 + kx + k(k−1) x2 + k(k−1)(k−2) x3 + … + k(k−1)…(k−(n−1)) xn + … 2! 3! n!

Substituting k=1/3 into the series:

5 terms:

(x+1)^1/3 = 1 + x/3 - x^2/9 + 5x^3/81- 10x^4/243