We will use mathematical induction to prove the inequality.
For n = 1,
Thus, for n = 1
and,
holds for n = 1
Let the inequality condition hold for n = k, where k 1
--- (1)
For n = k + 1
As, is a probability value and it should lie between 0 and 1,
. So,
and hence the inequality holds for n = k + 1
Hence by mathematical induction,
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