Concept:1). We know that the rth term from the end in the expansion (a + b)n = (n ? r + 2)th term from the beginning of the expansion (a + b)n2). rth term for the binomial expression, (x + y)n, Tr = nCr-1 xn-r-1 yr-1 Calculation:In the expansion \(\left(x + \frac{1}{x}\right)^{2n} \),The (n + 1)th term from the end = (2n ? n ? 1 + 2) = (n + 1)th term from the beginning.We know that, Tr = nCr-1 xn-r-1 yr-1Now, the tn+1 term is given by ? Tn+1 = 2nCn (x)2n-n (1/x)n? Tn+1 = 2nCn (x)2n-n-n? Tn+1 = 2nCn? Tn+1 = 2nCn or C(2n, n)