Now let the production function for output be Y t = A t K t L

Now let the production function for output be Y_t = A_tK_t^α L^1−α_yt. That is, we’ve made the exponent on capital a parameter (α) rather than keeping it as a specific number. Notice that this affects the exponent on labor as well, in order to preserve constant returns to objects.
(a) Solve for the growth rate of output per person along a balanced growth path. Explain how it relates to the solution of the model considered in the appendix.
(b) Solve for the level of output per person along a balanced growth path. Explain how it relates to the solution of the model considered in the appendix.
(c) The formula for a geometric series is 1 + α + α² + α³+ …. = 1 / (1 – α)  if α is some number between 0 and 1. How and why is this formula related to your answers to parts (a) and (b)?