Letγ_n =sum from k=1 to n of 1/k- log n and γ = lim γ_n.Robert M. Young [1] proved that 1/2n+2<γ_n-γ<1/2n.In a different context, I recently found a nice trick, which enables me to give a quick proof of (1), and indeed to improve on it. Rather than use the series for log (1 + x) with x =1 I shall use the formula with x =1+1. As you will see, it gives a series of positive terms. The advantage of having a series of positive terms is that it is relatively easy to estimate the sum, that is, to give upper and lower bounds for the sum.
展开▼
