Suppose `x `and `y` are two real numbers such that the rth mean between `x`and `2y` is equal to the rth mean between `2x` and `y` when `n` arithmetic means are inserted between them in both the cases. Show that `(n+1)/r-y/x=1.`

Explanation

To solve the problem, we need to show that:

\[ \frac{n+1}{r} - \frac{y}{x} = 1 \]

Given that the rth mean between \(x\) and \(2y\) is equal to the rth mean between \(2x\) and \(y\) when \(n\) arithmetic means are inserted in both cases.

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