If 1/a, 1/b, 1/c are in A.P., prove that: a(b+c), b(c+a), c(a+b) are in A.P.

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If 1/a, 1/b, 1/c are in A.P., prove that: (b+c)/a, (c+a)/b, (a+b)/c are in A.P. If 1/a, 1/b, 1/c are in A.P., prove that: (b+c)/a, (c+a)/b, (a+b)/c are in A.P.
If ` 1/a,1/b,1/c` are in AP, prove that (i) ((b+c))/a, ((c+a))/b,((a+b))/c` are in AP. If ` 1/a,1/b,1/c` are in AP, prove that (i) ((b+c))/a, ((c+a))/b,((a+b))/c` are in AP.
If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P., prove that a, b, c are in A.P. If a(1/b+1/c), b(1/c+1/a), c(1/a+1/b) are in A.P., prove that a, b, c are in A.P.
if a(1/b + 1/c) , b (1/c + 1/a) , c (1/a + 1/b ) are in AP ., prove that a,b,c are in AP. if a(1/b + 1/c) , b (1/c + 1/a) , c (1/a + 1/b ) are in AP ., prove that a,b,c are in AP.
"If `1/a ,1/b ,1/c`are in A.P. prove that: `(b+c)/a ,(c+a)/b ,(a+b)/c`are in A.P." "If `1/a ,1/b ,1/c`are in A.P. prove that: `(b+c)/a ,(c+a)/b ,(a+b)/c`are in A.P."
If 1/a, 1/b, 1/c are in A.P., prove that : b+c/a, c+a/b, a+b/c are also in A.P. If 1/a, 1/b, 1/c are in A.P., prove that : b+c/a, c+a/b, a+b/c are also in A.P.
If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`are in A.P., prove that a, b, c are in A.P. If a `(1/b+1/c),b(1/c+1/a),c(1/a+1/b)`are in A.P., prove that a, b, c are in A.P.
IF `1/a,1/b,1/c` are in AP then prove that `(b+c)/a,(a+c)/b,(a+b)/c` are in AP IF `1/a,1/b,1/c` are in AP then prove that `(b+c)/a,(a+c)/b,(a+b)/c` are in AP