What is the HM of 1,1/2,1/3.....1/n?

Answer 1

Ezekiel Anderson

#2/(n+1)#

To find the harmonic mean of a set of numbers, we

Now, for #1,1/2,1/3,...,1/n#

The required harmonic mean is #2/(n+1)#

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Answer 2

Emery Adams

The harmonic mean (HM) of a set of numbers is calculated by dividing the number of elements by the sum of their reciprocals. For the given sequence $1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{n}$ , the harmonic mean can be found as follows:

Calculate the sum of the reciprocals of the numbers: $1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}$ .
Divide the number of elements (which is $n$ ) by the sum obtained in step 1.

So, the harmonic mean of the sequence $1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{n}$ is $\frac{n}{1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{n}}$ .

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.