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Question

If a,b,c are in H.P and n>1, show that an+cn>2bn.

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Solution

Let anandcn be two numbers

AM>GM

then an+cn2>(an.cn)12

an+cn>2(a.c)n2 ---- (1)

Also G.M.>H.M.

i.e. ac>bacn2>bn ---- (2)

Hence from (1) and (2) an+cn>2bn

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