Chapter 8.8 Problem 23
write out the first 5 terms of the Binomial series with the given k-value. k=4
Given a real number \(k\) and nonnegative interger \(n\), the number \(4\), read “\(k\) choose \(n\)”, is given by \[f(x) = (1 + x)^4 \]
\(f(x) = (1 +x)^{4x} = 1 + 4x + 6x^2 + 4x^3 + x^4\)
This was the example 264 in the text.
we know that \(k = 4\) and that the maclaurin series for \(f(x) = (1 + x)^k\) is
\[1 + k + (1+x)^k + k(1+x)^{k-1} + k(k-1)(1+x)^{k-2}\]