Write out the first 5 terms of the Binomial series with the given k-value.
When \(k = 4\), the first 5 terms of the Binomial series with the given k-value are as follows:
\(1+k+{ \left( 1+x \right) }^{ k }+k{ \left( 1+k \right) }^{ k-1 }+k\left( k-1 \right) { \left( 1+x \right) }^{ k-2 }\)