textbook: Apex Calculus 1
In Exercises 21-24, write out the first 5 terms of the Binomial series with the given k-value
\(f(x) = (1+x)^{k}\) when \(k = 4\)
\[k^{0}x^{0} + k^{1}x^{1} + \frac{k(k-1)}{2!}x^2 + \frac{k(k-1)(k-2)}{3!}x^3 + \frac{k(k-1)(k-2)(k-3)}{4!}x^4\]
\[(1\times 1)+({ 4 }x)+(\frac { 4(4-1) }{ 2! } x^{ 2 })+(\frac { 4(4-1)(4-2) }{ 3! } x^{ 3 })+(\frac { 4(4-1)(4-2)(4-3) }{ 4! } x^{ 4 })\] \[1+({ 4 }x)+(6x^{ 2 })+(4x^{ 3 })+(x^{ 4 })\]