Sequence And Series Question 23
Question: If the harmonic mean between $ a $ and $ b $ be $ H $ , then $ \frac{H+a}{H-a}+\frac{H+b}{H-b}= $
[AMU 1998]
Options:
A) 4
B) 2
C) 1
D) $ a+b $
Show Answer
Answer:
Correct Answer: B
Solution:
Putting $ H=\frac{2ab}{a+b} $ $ \frac{H+a}{H-a}+\frac{H+b}{H-b}=\frac{2(H^{2}-ab)}{(H-a)(H-b)}=\frac{2[ \frac{4ab}{{{(a+b)}^{2}}}-ab ]}{[ \frac{4ab}{{{(a+b)}^{2}}}-ab ]}=2 $ . Trick: Let $ a=1,\ H=\frac{1}{2} $ and $ b=\frac{1}{3} $ , then $ \frac{H+a}{H-a}+\frac{H+b}{H-b}=\frac{3/2}{-1/2}+\frac{5/6}{1/6}=2 $ .
BETA
