a) Prove that for n∈N,
k=2∑nk1≤ln(n)≤k=1∑n−1k1.
b) Prove that the limit
γ:=n→∞lim((k=1∑nk1)−ln(n))
exists. This constant is known as the Euler--Mascheroni constant. It is not known if this constant is rational or not. It is approximately γ≈0.5772.