39. Prove the formula in (7.147) using mathematical induction. (Hint: The formula is proved for n ¼ 1; 2 already. Assume it to be true for n, and show it is true for n þ 1 by applying the assumed formula to the two values of the option at time 1, LðSu 1 Þ

and LðSd 1 Þ. Recall exercise 33.)