Vivekanand Vellanki
0

Not sure if I understood the question.

For an expression like \left(x+a\right)^n, the term independent of x is ^nC_0\cdot a^n because this represent the case where x is chosen 0 times.

For an expression like \left(x+\frac{1}{x}\right)^{2n}, the term independent of x is when x is chosen n times. Hence, the term independent of x is ^{2n}C_n\cdot x^n\cdot\left(\frac{1}{x}\right)^n