Chapter 6.3, Problem 1SP

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.

1. Write the Macbunn polynomials p₀(x), p₁(x), P₂(x). p₃(x), p₄(x) for e^x. Evaluate P₀(1), P₁(1).P₂(1), P₃(1), P₄(1) to estimate e.