prove that the term independent of x in the expansion of (x+1/x)^2n is 1.3.5......(2n-1)/n! .2^n

Question

prove that the term independent of x in the expansion of
(x+1/x)^2n is 1 3 5 (2n-1)/n! 2^n

Anuradha Sharma · Accepted Answer

Since there are 2n+1 term so by looking at the expansionx+1x2n we can say that term independent of x will be middle termSo in x+1x2n the middle term will be = 2nCn=2n!n!×n!=1
2 3 4 n n+1 2nn!×n!=1 3 5 2n-12 4 6 2nn!×n!=1 3 5
2n-1×2n1 2 3 4 nn!×n!=1 3 5
2n-1×2nn!n!×n!=1 3 5 2n-1×2nn!=