Discrete varying insurance: for increasing whole life in discrete time, the present value is given by a sum. If the policy is term with term length n, what is the upper limit of the summation?

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In discrete-time valuation, the present value of a term insurance benefit is a sum over all possible times when death could occur while the policy is in force. Time is usually indexed so that t = 0 corresponds to the end of the first year, t = 1 to the end of the second year, and so on. If the term length is n years, the policy pays only for deaths that occur within those n years, i.e., up to the end of year n. The end of year n corresponds to t = n−1 in this indexing, so the summation runs from t = 0 up to t = n−1. Beyond that, there are no benefits to discount, since the term expires.

Therefore, the upper limit of the summation is n−1. If the term were not restricted, like in a whole life policy, the sum would extend indefinitely (to infinity).