Question

If H₁, H₂, H₃ ……..H_2n+1 are in H.P. then $\sum _ { i = 1 } ^ { 2 n } ( - 1 ) ^ { i }$ $\left( \frac{H_{i} + H_{i + 1}}{H_{i} - H_{i + 1}} \right)$is equal to –

• A. 2n –1
• B. 2n + 1
• C. 2n
• D. 2n + 2

Answer 1

Answer: (C)

2n

Answer 2

Let $\frac{1}{H_{i + 1}}$– $\frac{1}{H_{i}}$= k

\ $\sum _ { i = 1 } ^ { 2 n } ( - 1 ) ^ { i }$ $\left( \frac{H_{i} + H_{i + 1}}{H_{i} - H_{i + 1}} \right)$

= $\left( \frac{1}{H_{i + 1}} + \frac{1}{H_{i}} \right)$= 2n