Discussion Forum

If the coefficients of $(2r+1)^{th}$ term and $(r+1)^{th}$ term in the expansion  of $(1+x)^{42}$ are equal then r can be

Answer:

Explanation:

We have, $(1+x)^{42}$

        $T_{2r+1}=^{42}C_{2r} x^{2r}$

 $T_{r+1}= ^{42}C_{r}x^{r}$

Coefficient  of $(2r+1)^{th}$  and $(r+1)^{th}$ term are equal 

$\therefore$     $^{42}C_{2r}= ^{42}C_{r}$

$\therefore$   2r+r=42    $[ \because   ^{n}C_{x}=^{n}C_{y} \Rightarrow x+y=n]$

 $\Rightarrow$    r=14