The sum of the first n terms of a harmonic progression is given by which of the following formulas?

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Q: The sum of the first n terms of a harmonic progression is given by which of the following formulas?

Solution: The sum of the first n terms of a harmonic progression can be expressed as 2n/(a+b) where a and b are the first two terms.

Steps: 7

Step 1: Understand what a harmonic progression (HP) is. A harmonic progression is a sequence of numbers where the reciprocals of the terms form an arithmetic progression (AP).
Step 2: Identify the first two terms of the harmonic progression. Let's call the first term 'a' and the second term 'b'.
Step 3: Recall that the sum of the first n terms of a harmonic progression can be derived from the sum of the first n terms of the corresponding arithmetic progression formed by the reciprocals of the terms.
Step 4: The formula for the sum of the first n terms of an arithmetic progression is given by S_n = n/2 * (first term + last term).
Step 5: For the harmonic progression, the first term is 1/a and the second term is 1/b. The last term in the first n terms will depend on the pattern of the HP.
Step 6: After deriving the sum from the arithmetic progression, you will find that the sum of the first n terms of the harmonic progression can be simplified to the formula 2n/(a+b).
Step 7: Conclude that the sum of the first n terms of a harmonic progression is given by the formula 2n/(a+b).