Which of the following is NOT a property of harmonic progressions?
Practice Questions
Q1
Which of the following is NOT a property of harmonic progressions?
The sum of the first n terms is finite.
The terms can be negative.
The terms can be fractions.
The terms can be irrational.
Questions & Step-by-Step Solutions
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.
