discussion 14

#In Exercises 21 – 24, write out the first 5 terms of the Binomial series with the given k-value.

x=2

# Find the first 5 terms of the Binomial series: 

#1.

k = 1/2
term <- 1+ k * x + (k * (k-1) / 2) * x^2 +  (k * (k-1) * (k-2) / 6) * x^3 + (k * (k-1) * (k-2) * (k-3) / 24) * x^4

#2.

k = -1/2
term <- 1+ k * x + (k * (k-1) / 2) * x^2 +  (k * (k-1) * (k-2) / 6) * x^3 + (k * (k-1) * (k-2) * (k-3) / 24) * x^4

#3.

k = 1/3
term <- 1+ k * x + (k * (k-1) / 2) * x^2 +  (k * (k-1) * (k-2) / 6) * x^3 + (k * (k-1) * (k-2) * (k-3) / 24) * x^4

#4.

k = 4
term <- 1+ k * x + (k * (k-1) / 2) * x^2 +  (k * (k-1) * (k-2) / 6) * x^3 + (k * (k-1) * (k-2) * (k-3) / 24) * x^4