The term independent of x in:

{ (1+x)^m [(x+1)/x]^n }

=(((1+x)^m)((1+x)^n))/x^n

=((1+x)^(m+n))/x^n

Expanding the above term using bionomial theorm

=(^m+n C₀₍x^0)+...+^m+n C_n(x^n)+...+^m+n C_m+n(x^(m+n)))/x^n

Only one term in int the above expansion will give a constant or independent on division with x^n

i.e. =^m+n C_n(x^n) 

So the answer is ^m+n Cn

Hi Aditya,

The given expression is (1+x)^m+n/xⁿ.

So let's find the co-eff of x^n in (1+x)^m+n, which is ^m+nC_n ----------(which is also equal to ^m+nC_m, becos ^NC_r = ^NC_N-r.)

Best Regards,

Ashwin (IIT Madras).