Question 21

Mathematics Sequence And Series Medium

If \(H\) is the Harmonic mean between \(P\) and \(Q\), then \(\frac{H}{P}+\frac{\mathrm{H}}{Q}\) is

(A) 2
(B) \(\frac{P+Q}{Q}\)
(C) \(\frac{P Q}{P+Q}\)
(D) None of these
View Dynamic Solution & Explanation
Correct Solution: Option A

Step-by-step Solution:

\(P, H, Q\) are in H.P. \[\] \(\frac{1}{P}, \frac{1}{H}, \frac{1}{Q}\) are in A.P. \[\] \(\frac{2}{H}=\frac{1}{P}+\frac{1}{Q} \Rightarrow 2=\frac{H}{P}+\frac{H}{Q}\) \[\] Choice (A)\[\]