Compute e in R - Jing Ma

The Taylor’s formula to approximate e - the natural logarithmic base:

$e = 1 + \sum_{k=1}^\infty \frac{1}{k!}$

that is:

$e = \text{1} + \frac{1}{\text{1!}} + \frac{1}{\text{2!}} + \frac{1}{\text{3!}} + \ldots$

We can deal with this problem using R language:

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s = 1.0             # initial part
x = 1               # the numerator 1
k = 0               # iterator

repeat {
  k <- k + 1        # current iterator
  x <- x / k        # the fractional part
  s <- s + x        # sum the two parts
  if (x < 1e-10) {  # control the accuracy
    break
  }
}

stringr::str_glue("After {k} iterations, the resuling e is: {s}")

## After 14 iterations, the resuling e is: 2.71828182845823