Dwindling powers

Algebra Level 4

The expression \((1+\sqrt{x})^n\) is expanded in decreasing powers of \(x\). If the fourth term can be expressed in terms of \(x^2\), find the value of \(\frac{p}{q+r}\).

Details:

\(p\) = sum of coefficients of all terms except first and last term

\(q\) = coefficient of second term

\(r\) = coefficient of fourth term

Hint:

You need to find the value of \(n\) first.

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