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

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Question

(A) Let the two numbers be $a = 3$ and $b = \frac{6}{13}$.The $n$-th $H.M.$ between $a$ and $b$ is given by the formula:$H_n = \frac{(n+1)ab}{na + b}$

Vedclass · Accepted Answer

$\frac{63}{120}$

Vedclass · Answer

(A) Let the two numbers be $a = 3$ and $b = \frac{6}{13}$.The $n$-th $H.M.$ between $a$ and $b$ is given by the formula:$H_n = \frac{(n+1)ab}{na + b}$For the sixth $H.M.$,$n = 6$:$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{18 	imes 13 + 6}{13}}$$H_6 = \frac{126}{234 + 6} = \frac{126}{240}$Simplifying the fraction by dividing both numerator and denominator by $2$:$H_6 = \frac{63}{120}$

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

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