Question

State true or false.

In the expansion of ${\left(1+a\right)}^{m+n}$, then coefficients of $a^m$and$a^n$ are equal.

• A. True
• B. False

Answer 1

The correct option is A True

$(1+a{)}^{m+n}$, coefficients of $a^m$ and $a^n$ are equal

Since $T_{r+1}={}^{m+n}Cr{a}^{\text{r}}$ (rth term)

Put $r=m$

$m+nCm{a}^m$ and Put $r=n$

$m+n{C}_n{a}^n=m+n{C}_{\text{m+n-n}-n}{a}^n={}^{m+n}{C}_m{a}^n$

So both are equal and coefficients