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.

Question

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.

sudhir pal · Answer

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 that q 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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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.

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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.

1 Answers

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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.