Mathematics - Binomial Theorem Question with Solution | TestHub

Let$\left(1-x+x^2..\right)\left(1+x+x^2\dots \right)=a_0+a_1\times a_2{x}^2+\dots$
Put$x=1$,
$1\left(2n+1\right)=a_0+a_1+a_2+..a_{2n} \dots \left(2\right)$
Put$x=-1$
$\left(2n+1\right)\times 1=a_0-a_1+a_2+..a_{2n} \dots \left(2\right)$
From$\left(1\right)+\left(2\right)$
$4n+2=2\left(a_0+a_2+\dots \right)$
$=2\times 61$
$\Rightarrow 2n+1=61\Rightarrow n=30$