The sixth H.M. between 3 and frac{6}{13} is | vedclass

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Question

(A) The formula for the $n^{th}$ Harmonic Mean $(H.M.)$ between two numbers $a$ and $b$ is given by $H_n = \frac{(n+1)ab}{na+b}$.Here,$a = 3$,$b = \fr

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$\frac{63}{120}$

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(A) The formula for the $n^{th}$ Harmonic Mean $(H.M.)$ between two numbers $a$ and $b$ is given by $H_n = \frac{(n+1)ab}{na+b}$.Here,$a = 3$,$b = \frac{6}{13}$,and $n = 6$.Substituting these values into the formula:$H_6 = \frac{(6+1) 	imes 3 	imes \frac{6}{13}}{6 	imes 3 + \frac{6}{13}}$$H_6 = \frac{7 	imes 3 	imes \frac{6}{13}}{18 + \frac{6}{13}}$$H_6 = \frac{\frac{126}{13}}{\frac{234+6}{13}}$$H_6 = \frac{126}{240}$Simplifying the fraction by dividing both numerator and denominator by $2$,we get:$H_6 = \frac{63}{120}$.

The sixth $H.M.$ between $3$ and $\frac{6}{13}$ is

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