The term independent of x in: { (1+x)^m [(x+1)/x]^n }

The term independent of x in:

{  (1+x)^m [(x+1)/x]^n  }


2 Answers

Swapnil Saxena
102 Points
11 years ago



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

Ashwin Muralidharan IIT Madras
290 Points
11 years ago

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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