MATH1061/7861, Wed 2 Sep 2020
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Question 1. Consider the sequence defined by the explicit formula: ai = (−1)i / i ! for each integer i ≥ 0. A. Write out the first five terms of this sequence, and guess a recurrence relation for the sequence. B. Show that this sequence satisfies your recurrence relation.
C. Write down a recursive definition of this sequence.
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Question 2. A binary string is a sequence of 0s and 1s, such as 0010110. Let S be the set of binary strings defined recursively
BASE
The questions:
A. Is 1101 ∈ S ? Why/why not?
B. Is 0110 ∈ S ? Why/why not?
C. Find a way to precisely describe all strings in S, without using recursion, and prove your answer correct.
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