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Prove that 2/(b+c)+2/(c+a)+2/(a+b)<1/a+1...

Prove that `2/(b+c)+2/(c+a)+2/(a+b)<1/a+1/b+1/c ,w h e r ea ,b ,c>0.`

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Using A.M.`gt` H.M we get
`((1)/(a) + (1)/(b))/(2) gt (2)/(a + b), ((1)/(b) + (1)/(c ))/(2) gt (2)/(b + c)` and `((1)/(c c ) + (1)/(a))/(2) gt (2)/(c + a)`
Adding we get
`(1)/(a) + (1)/(b) + (1)/(c ) gt (2)/(a + b) + (2)/(b + c) + (2)/(a + c)`
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