Chapter 8.8, Exercise # 23

Write out the first 5 terms of the Bionomial Series with the k-value, k=4

Given a real number k and nonnegative integer n, the number 4, read “k choose n”, is given by

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

Since k = 4
The Maclaurin Series for:

\(f(x) = (1+x)^4 =\)
\(1 + k + (1+x)^k + k(1+x)^{k-1} + k(k-1)(1+x)^{k-2}\)