Prove that e is an irrational number using the following argument by contradiction.
Suppose that e = M/N, where M, N are nonzero integers.
(a) Show that M! e⁻¹ is a whole number.
(b) Use the power series for ƒ(x) = e^x at x = −1 to show that there is an integer B such that M! e⁻¹ equals

(c) Use your knowledge of alternating series with decreasing terms to conclude that 0 −1 − B|

Transcribed Image Text:

B + (-1)M+1 1 M+1 1 (M+1)(M + 2) +