The middle term in the expansion of (x+1x)10 is

The middle term in the expansion of a binomial expression can be found using the formula for the nth term in a binomial expansion, which is given by:

T(n+1) = nCr * (a^(n-r)) * (b^r)

where:

• n is the power to which the binomial is raised (in this case, 10),
• r is the term number (for the middle term of an expansion with an even power, this will be n/2),
• a and b are the terms in the binomial (in this case, x and 1/x respectively),
• nCr is the combination of n items taken r at a time.

For the expansion of (x + 1/x)^10, the middle term is the 6th term (10/2 + 1), so we substitute n = 10, r = 5, a = x, and b = 1/x into the formula:

T(6) = 10C5 * (x^(10-5)) * ((1/x)^5)

This simplifies to:

T(6) = 252 * x^5 * x^-5

The x^5 and x^-5 cancel out, leaving:

T(6) = 252

So, the middle term in the expansion of (x + 1/x)^10 is 252.