Solve `(x - 1)^n =x^n`, where n is a positive integer.

Find the co-efficient of 1/x of the expansion of (1+x)^n(1+1/x)^n where n is a positive integer.

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.

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

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

Write the middle term in the expansion of : (1+x)^(2n) , where n is a positive integer.

If ((1+i)/(1-i))^x=1 then (A) x=2n+1 , where n is any positive ineger (B) x=4n , where n is any positive integer (C) x=2n where n is any positive integer (D) x=4n+1 where n is any positive integer

Prove that the function f(x)=x^n is continuous at x = n , where n is a positive integer.

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.