$$\sum_{k=1}^{25}6\frac{^{24}P_{k-1}}{^{30}P_{k}}=1$$
$$\sum_{k=1}^{25}6k\frac{^{24}P_{k-1}}{^{30}P_{k}}=\frac{31}{7}$$
This question come from a distribution. First equation is the sum of probability. Second equation is the expected value.
Is that any general way to calculate these two equation?