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If a ,b ,ca n dd are in H.P., then prove...

If `a ,b ,ca n dd` are in H.P., then prove that `(b+c+d)//a ,(c+d+a)//b ,(d+a+b)//c` and `(a+b+c)//d` , are in A.P.

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a,b,c, and d are in H.P.
`rArr1/a,1/b,1/c,1/d` are in A.P.
`rArr(a+b+c+d)/a,(a+b+c+d)/b,(a+b+c+d)/c,(a+b+c+d)/d` are in A.P.
`rArr1+(b+c+d)/a,(a+c+d)/b+1,(a+b+d)/c+1,(a+b+c)/d+1` are in A.P.
`rArr (b+c+d)/a,(a+c+d)/b,(a+b+d)/c,(a+b+c)/d` are in A.P.
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