Exercise 8.8.5

Key Idea 32 gives the nth term of the Taylor series of common func ons. In Exercises 3 – 6, verify the formula given in the Key Idea by finding the first few terms of the Taylor series of the given func on and iden fying a pa ern.

require(pracma)
## Loading required package: pracma
x = function(x) {1/(1-x)}

c = 0
n = 8

taylor(x, c, n)
## [1] 1.022551 1.007014 1.001710 1.000293 1.000029 1.000003 1.000000 1.000000
## [9] 1.000000