Chapter 6.3, Problem 4SP

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.

4. Write down the formula for the nth Maclaurin polynomial p_n(x) for e^xand the corresponding remainder R_n(x). Show that sn!R_n(1) is an integer.