If b-c-a-a- c-a-b-b- a-b-c-c are in A-P- then prove that 1-a- 1-b- 1-c are also in A-P-

Given b+c a/a, c+a b/b, a+b c/c are in A.P.Add 2 to each term ⇒ b+c+a/a, c+a+b/b, a+b+c/c are in A.P.divide each by a+b+c⇒1/a, 1/b, 1/c a ...

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nth Term of A.P

If b+c-a/a,...

Question

If $\frac{b + c - a}{a}, \frac{c + a - b}{b}, \frac{a + b - c}{c}$ are in A.P., then prove that $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are also in A.P.

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