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.

Explanation

To prove that if \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in Arithmetic Progression (A.P.), then \( \frac{b+c}{a}, \frac{c+a}{b}, \frac{a+b}{c} \) are also in A.P., we can follow these steps:

### Step 1: Use the definition of A.P.
Since \( \frac{1}{a}, \frac{1}{b}, \frac{1}{c} \) are in A.P., we can use the property of A.P. which states that the middle term is the average of the other two terms. Thus, we have:
\[ \frac{1}{b} - \frac{1}{a} = \frac{1}{c} - \frac{1}{b} \]

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