The middle term in the expansion of (1+x)2n  is:

Given expansion (1+x)2n  is We have general term in the expansion (x+a)n (∴  Tr+1= nCr xn−r (a)r  be the expansion of (x+a)n) Here, index =2n , which is an even number, therefore, the middle term will be (n+1)th  term.Now, Tn+1= 2nCn(1)2n−nxn Tn+1= 2nCn(1)2n−nxn=2n!n!n!xn  (∴nCr=n!(n−r)! r!)