If the p^{th},q^{th},and r^{th} terms of a ha | vedclass

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(B) Let the harmonic progression be $\frac{1}{a}, \frac{1}{a+d}, \frac{1}{a+2d}, \dots$Then,$u = \frac{1}{a+(p-1)d}$,$v = \frac{1}{a+(q-1)d}$,and $w =

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(B) Let the harmonic progression be $\frac{1}{a}, \frac{1}{a+d}, \frac{1}{a+2d}, \dots$Then,$u = \frac{1}{a+(p-1)d}$,$v = \frac{1}{a+(q-1)d}$,and $w = \frac{1}{a+(r-1)d}$.This implies $\frac{1}{u} = a+(p-1)d$,$\frac{1}{v} = a+(q-1)d$,and $\frac{1}{w} = a+(r-1)d$.Subtracting these equations,we get:$\frac{1}{u} - \frac{1}{v} = (p-q)d \implies \frac{v-u}{uv} = (p-q)d$$\frac{1}{v} - \frac{1}{w} = (q-r)d \implies \frac{w-v}{vw} = (q-r)d$$\frac{1}{w} - \frac{1}{u} = (r-p)d \implies \frac{u-w}{wu} = (r-p)d$Multiplying the terms,we observe that $(q-r)vw + (r-p)wu + (p-q)uv = 0$.

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a harmonic progression are $u$,$v$,and $w$ respectively,then the value of $(q - r)vw + (r - p)wu + (p - q)uv$ is equal to:

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