Calculus

Let re is the spot rate for a t-year maturity zero coupon bond. (i) Find an expression for fik-1,k] in terms of the rt's. (ii) Show that (1 + fo,1) (1 + f[1,2]) . . . (1 + f[k-1,k]) = (1 + rx)k for k = 1, 2, ..., n. (iii) Show that d fk - 1, k] > 0 and d drk . drk-1 fThe - 1, K] k-1, then f(k -1,1) >k