Find `(n+1)^(th)` term in the expansionof `(x+1/x)^(2n)`

Find the 6th term in the expansion of (3x^2-1/3x)^8

The coefficients of the (r-1)^(th) , r^(th) and (r+1)^(th) terms in the expansion of (x + 1)^n are in the ratio 1:3:5. Find n and r.

Find 5th term in the expansion of (2x^2-1/3x)^11 .

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

Find the middle terms in the expansion of : (x/y+y/x)^(2n+1) .

Find the (n+ 1)th term from the end in the expansion of (x-1/x)^(3n) .

If the greatest term in the expansion of (1+x)^(2n) has the greatest coefficient if and only if xepsilon(10/11, 11/10) and the fourth term in the expansion of (kx+ 1/x)^m is n/4 then find the value of mk.

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

Show that the middle term in the expansion of (1+x)^(2n) is (1.3.5….(2n-1))/(n!) 2^(n)x^(n) , where n is a positive integer.