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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  }

Grade:11

2 Answers

Swapnil Saxena
102 Points
9 years ago

=(((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

Ashwin Muralidharan IIT Madras
290 Points
9 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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