R: approximating `e = exp(1)` using `(1 + 1 / n) ^ n` gives absurd result when `n` is large

Question

So, I was just playing around with manually calculating the value of e in R and I noticed something that was a bit disturbing to me.

The value of

Answer 1

You might also try the Taylor series approximation to exp(1), namely

e^x = \sum_{k = 0}{\infty} x^k / k!

Thus we can approximate e = e^1 by truncating this sum; in R:

sprintf('%.20f', exp(1))
# [1] "2.71828182845904509080"
sprintf('%.20f', sum(1/factorial(0:10)))
# [1] "2.71828180114638451315"
sprintf('%.20f', sum(1/factorial(0:100)))
# [1] "2.71828182845904509080"