Life Contingencies School Level Maths Proof 2

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    Richard Purvey
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    Life Contingencies School Level Maths Proof 2

    Starting with the two equations:
    <p style=”text-align: center;”>1. e^(-delta)=v and</p>
    2. (1-d(m)/m)^m=v, show that lim m→infinity d(m)=delta.

    Method

    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.

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