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$If H_{P} H_{2}, \dots . H_{20} harmonic means between 2 and 3, then \frac{H_{1} + 2}{H_{1} - 2} + \frac{H_{20} + 3}{H_{20} - 3}$

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Correct option is C

2,H1,H2…….H20,3 are in H. P H1+2H1−2+H20+3H20−3=12+1H112−1H1+13+1H2013−1H20 =12+12+d12−d−12+13+13−d13+d−13 =1+d−d+23−dd=23−1d−2 =2×21−2 =40

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If HPH2,….H20 harmonic means between 2 and 3, then H1+2H1−2+H20+3H20−3

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$If H_{P} H_{2}, \dots . H_{20} harmonic means between 2 and 3, then \frac{H_{1} + 2}{H_{1} - 2} + \frac{H_{20} + 3}{H_{20} - 3}$