$$sum_{k=1}^{25}6frac{_{24}P_{k-1}}{_{30}P_{k}}=1$$

$$sum_{k=1}^{25}6kfrac{_{24}P_{k-1}}{_{30}P_{k}}=frac{31}{7}$$

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?