UPSC CDS 2 2022 Math Paper

Harmonic mean (HM): If a, b \& c are in AP then,
1∕a,1∕b,1∕c are in harmonic progression (HP).
If H is the harmonic mean of a\&b, then
H=‌

2

1 a +‌ 1 b

or H=‌

2‌ab

a+b

Calculation:
We have,
x is the harmonic mean of y and z
⇒x=‌

2‌yz

y+z

⇒xy+xz=2‌yz
⇒xy+xz−2‌yz=0
∴ If x is the harmonic mean between y and z, then xy+xz−2yz=0.