Write a recursive method called sumTo that accepts an integer parameter n and returns a real number representing the sum of the first n reciprocals. In other words, sumTo(n) returns (1 1/2 1/3 1/4 ... 1/n). For example, sumTo(2) should return 1.5. The method should return 0.0 if it is passed the value 0 and throw an IllegalArgumentException if it is passed a value less than 0.

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?