Consider the following non-level perpetuity. The payment is received at the end of year each year. The payments of the first 10 years are $K per year. From the 11-th year, the payments become $2K per year. Assume that the money grows at an effective annual rate i. Express the present value of this non-level perpetuity as a function of K and i.

You may use symbols ani,a ni,sni,s ni (n finite, or ) in your expression.