the angle symbol just means there are k periods

A perpetuity-due has a payment once every k years. The j-th payment is j. Show that this perpetuity has present value equal to (1/ia_k i)^2. Let k divide n. The accumulated value at the time of the last payment of an annuity lasting n interest periods, having a payment at the end of each k interest periods, and having the j-th payment be for an amount j is s_n i/a_k i - n/k/is_k i. The value of this annuity one payment period before the first payment is a_n i/a_k i - n/k upsilon^n/is_k