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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 Cn(x^n)+...+m+n Cm+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 Cn(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+nCn ----------(which is also equal to m+nCm, becos NCr = NCN-r.)
Best Regards,
Ashwin (IIT Madras).
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