The nth harmonic number is defined non-recursively as: 1 +1/2 + 1/3 + 1/4 + + 1/n. come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.

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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)?

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