Homework 1 Solution

All algorithms/proofs should be in bullet form: step by step.

    1. Exercise 3, Page 22

    2. Exercise 4, on Page 22

    3. Exercise 6 on page 25

    4. Exercise 4 on page 67

    5. (a) Prove (by induction) that sum of the rst n integers (1+2+::::+mn) is n(n + 1)=2

        (b) What is 13 + 23 + 34 + ::: + n4 = ?? Prove your answer by induction.

    6. How many tries do you need (in the worst case) in the two egg problem when there are 200 steps? what about n steps?
























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