Which of the following is NOT a property of harmonic progressions?

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Question: Which of the following is NOT a property of harmonic progressions?

Options:

Correct Answer: The sum of the first n terms is finite.

Solution:

The sum of the first n terms of a harmonic progression diverges as n approaches infinity, hence it is not finite.

Which of the following is NOT a property of harmonic progressions?

Which of the following is NOT a property of harmonic progressions?

Step 1: Understand what a harmonic progression is. A harmonic progression is a sequence of numbers where the reciprocals of the numbers form an arithmetic progression.
Step 2: Recall the properties of harmonic progressions. One key property is that the sum of the first n terms diverges as n approaches infinity.
Step 3: Recognize that 'diverges' means the sum does not settle at a finite number; it keeps increasing without bound.
Step 4: Identify the question's requirement: we need to find which option is NOT a property of harmonic progressions.
Step 5: Compare the options given in the question with the known properties of harmonic progressions.
Step 6: Conclude that since the sum of the first n terms diverges, it is indeed NOT finite, which aligns with the short solution provided.

No concepts available.