3.5 Complete the proof of Stirling’s formula. Note that there are various proofs of this famous approximation. For example, a standard proof involves the use of the Wallis formula:

∞

k=1

(2k)2

(2k − 1)(2k + 1)

= π

2

;

an alternative proof can be given via the CLT (e.g., Casella and Berger 2002, pp. 261). You are asked to find at least one complete proof of Stirling’s formula.