Q. 94.3( 72 Votes )

In the expansion of (1 + a)m+n, prove that coefficients of am and an are equal.

Answer :

The general term Tr+1 in the binomial expansion is given by Tr+1 = nCr an-r br

Here n= m+n , a = 1 and b= a


Putting the values in the general form


Tr+1 = m+nCr 1m+n-r ar


= m+nCr ar………….1

Now we have that the general term for the expression is,

Tr+1 =  m+nCr ar
Now, For coefficient of am

Tm+1 =  m+nCm am
Hence, for coefficient of am, value of r = m

So, the coefficient is m+nCm

Similarly, Coefficient of an is m+nCn

m+nCm

And also,

m+nCn = 

The coefficient of am and an are same i.e.;


Hence proved.

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