In Exercises 21 – 24, write out the first 5 terms of the Binomial series with the given k-value.
\[k=4\]
Pulled from the text (pg489): When k is a positive integer, the Maclaurin series is finite. For instance, when k = 4, we have
\[f\left( x \right) ={ \left( 1+x \right) }^{ 4 }=1+4x+6{ x }^{ 2 }+4{ x }^{ 3 }+{ x }^{ 4 }\]
When k=4 and the maclaurin series for \(f\left( x \right) ={ \left( 1+x \right) }^{ k }\) is
\[1+k+{ \left( 1+x \right) }^{ k }+k{ \left( 1+k \right) }^{ k-1 }+k\left( k-1 \right) { \left( 1+x \right) }^{ k-2 }\]