Chapter 6.3, Problem 5SP

In this project. we use the Macburin polynomials for e^xto prove that e is irrational. The proof relies on supposing that e is rational and arriving a a contradiction. Therefore, in the following steps, we suppose e = r/s for some integers r and s where s ≠ 0.

5. Use Taylor’s theorem to write down an explicit formula for R_n(1). Conclude that R_n(1) ? 0, and therefore. sn!R_n(l) ?0.