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"If "(1)/(a+b),(1)/(2b),(1)/(b+c) are in...

`"If "(1)/(a+b),(1)/(2b),(1)/(b+c)` are in A.P., then prove that a, b, c are in G.P.

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To prove that \( a, b, c \) are in G.P. given that \( \frac{1}{a+b}, \frac{1}{2b}, \frac{1}{b+c} \) are in A.P., we can follow these steps: ### Step 1: Set up the condition for A.P. Since the terms \( \frac{1}{a+b}, \frac{1}{2b}, \frac{1}{b+c} \) are in A.P., we can write the condition for A.P.: \[ \frac{1}{2b} - \frac{1}{a+b} = \frac{1}{b+c} - \frac{1}{2b} \] ...
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