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If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers, prove that q cannot lie between p (n+1/n-1)^2 & p.

If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers, prove that q cannot lie between
p (n+1/n-1)^2 & p.

Grade:12

1 Answers

sudhir pal
askIITians Faculty 26 Points
7 years ago
we can use AM> GM> HM
lets p>0 that means p (n+1/n-1)^2 > p from above p > q (also can be proved for negative p)
hence we can say thatq cannot lie between p (n+1/n-1)^2 & p.
other solution is also attached
Thanks & Regards
Sudhir,
askIITians Faculty
Qualification.
IIT Delhi
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