Explanation:

Let's break down the question:

- The general term in the expansion of \((x + 1/x)^{2n}\) is:

\(T_{k+1} = \binom{2n}{k} x^{2n-k} (1/x)^k = \binom{2n}{k} x^{2n-2k}\)

- When writing terms in descending powers of \(x\), \(k\) increases as the exponent decreases.

- The first term (highest power) is for \(k = 0\), i.e. \(x^{2n}\).

Second term: \(k = 1\), next lower power, and so on.

- The \((n+1)^{th}\) term from the start (descending powers) happens when \(k = n\):

$$

T_{n+1} = \binom{2n}{n} x^{2n-2n} = \binom{2n}{n}

$$

Options explained:

- Option 1: \(C(2n, n)x\) – this would have an \(x\), but in position \(n+1\), exponent is 0.

- Option 2: \(C(2n, n-1)x\) – this is the previous term.

- Option 3: \(C(2n, n)\) – correct, as calculated above.

- Option 4: \(C(2n, n-1)\) – this is the next previous term.