Suppose that, when you die, the proceeds of a life insurance policy will be deposited into a trust fund that will earn 8% interest, compounded continuously. According to the terms of your will, the trust fund must pay to your descendants and their heirs c₁ dollars (total) at the end of the first year, c₂ dollars at the end of the second year, c₃ dollars at the end of the third year, and so on, forever. The amount that must be in the trust fund initially to make the kth payment is c_ke^-0.08k, the present value of the amount to be paid in k years. So the life insurance policy should pay a total of ∑^∞_{k = 1}c_ke^-0.08k dollars into the trust fund to provide for all the payments.

How large must the insurance policy be if c_k = 10,000(.9)^k for all k?