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Home  >>  CBSE XI  >>  Math  >>  Binomial Theorem
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In the expansion of $(1+a)^{m+n}$,prove that coefficient of $a^m$ and $a^n$ are equal.

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  • $T_{r+1}=(m+n)C_ra^r.$
  • $nC_r=nC_{n-r}$
Putting $r=m$
$T_{m+1}=(m+n)C_m$-----(1)
$\therefore$ Coefficient of $a^m=(m+n)C_m$
Again putting $r=n$
$T_{n+1}=(m+n)C_na^n$
Coefficient of $a^n=(m+n)C_n=(m+n)C_m$-----(2)
From (1) and (2) coefficient of $a^m$ is equal to $a^n$
Hence proved.
answered Jun 23, 2014 by sreemathi.v
 

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