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Question

The ratio of the coefficients of xm and xn in the expansion of (1 + x)m + n is ___________.

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Solution

For (1 + x)m + n
Tr+1 = m+nCr xr
for coefficient of xm, r = m
i.e coefficient is m+nCm
and for coefficient of xn, r = n
i.e. coefficient is m+nCn
Ratio of coefficient of xm to xn is m+nCmm+nCn=m+nCm+n-mm+nCn=m+nCnm+nCn=1


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