Find the Harmonic Mean (H.M.) of the sequence | vedclass

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(C) The given sequence is $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots, \frac{1}{17}$.Here,the number of terms $n = 16$.The harmonic mean $H.M.$ is g

Vedclass · Accepted Answer

$2/19$

Vedclass · Answer

(C) The given sequence is $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots, \frac{1}{17}$.Here,the number of terms $n = 16$.The harmonic mean $H.M.$ is given by the formula:$H.M. = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}$Substituting the values:$H.M. = \frac{16}{\frac{1}{1/2} + \frac{1}{1/3} + \dots + \frac{1}{1/17}}$$H.M. = \frac{16}{2 + 3 + 4 + \dots + 17}$The sum of the arithmetic progression $2, 3, \dots, 17$ is given by $S_n = \frac{n}{2}(a + l) = \frac{16}{2}(2 + 17) = 8 	imes 19 = 152$.Therefore,$H.M. = \frac{16}{152} = \frac{1}{9.5} = \frac{2}{19}$.

Find the Harmonic Mean $(H.M.)$ of the sequence $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots, \frac{1}{17}$.

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