A perpetuity is a periodic sequence of payments that continues forever. The capital value of the perpetuity is the sum of the present values of all future payments.

Consider a perpetuity that promises to pay $100 at the beginning of each month. If the interest rate is 12% compounded monthly, the present value of $100 in k months is 100(1.01)-k.

(a) Express the capital value of the perpetuity as an infinite series.

(b) Find the sum of the infinite series.