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If $l=1+a+a^2+ \dots$, $m=1+b+b^2+ \dots$, and $n=1+c+c^2+ \dots$, where $\mid a \mid <1, \: \mid b \mid < 1, \: \mid c \mid <1$ and $a,b,c$ are in arithmetic progression, then $l, m, n$ are in

  1. arithmetic progression
  2. geometric progression
  3. harmonic progression
  4. none of these
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Harmonic Progression is the answer.

Let us take a = 0.1, b = 0.2, c = 0.3. Then l = 10/9, m = 10/8, n = 10/7 which are in harmonic progression.
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