Final answer:
The sequence 1/2, 1, 1/3, 1/4 is not a subsequence of 1/n because the order of the terms does not match the natural progression of 1/n, where no terms are missing in a subsequence. In this specific case, the term 1/2 is missing between 1 and 1/3, thus breaking the subsequence pattern.
Step-by-step explanation:
To understand why the sequence 1/2, 1, 1/3, 1/4 is not a subsequence of 1/n, we need to look at the definition of a subsequence.
A subsequence is formed by deleting any number of elements (possibly none) from the original sequence, without changing the order of the remaining elements.
When you have the sequence 1/n, it represents the sequence 1/1, 1/2, 1/3, 1/4, and so on, where n takes on successive positive integer values.
In the sequence provided by the student, the second term is 1, which can be written as 1/1.
This is followed by the term 1/3. If this were a subsequence of the 1/n sequence, we would expect no term between 1/1 (or 1) and 1/3; however, 1/2 is missing between these two terms in the given sequence, which would be present in the natural sequence of 1/n.
Next, the term 1/4 makes sense to follow 1/3, but since 1/2 was skipped earlier, we cannot regard the original series as a subsequence of 1/n because the order has been disrupted.
Additionally, to clarify the concept with known examples: we know that one half of one half is one quarter, and one half of 2 must be 1, or that three thirds must be a whole one.
In this example, 1 is followed by 1/3, which breaks the potential subsequence as 1/2 is expected to be in between as per the sequence 1/n.