Life Contingencies School Level Maths Proof 2
Starting with the two equations:
1. e^(-delta)=v and
2. (1-d(m)/m)^m=v, show that lim m→infinity d(m)=delta.
Re-arranging equation 1. gives delta=-ln(v) and re-arranging equation 2. gives d(m)=m*(1-v^(1/m)), meaning that lim m→infinity d(m)=lim m→infinity m*(1-v^(1/m)), which, after using an Online Limits Calculator, is found to equal –ln(v) which equals delta.