Question 25
Given that
$$x+(1+x)^2+(1+x)^3+\cdots+(1+x)^n=a_0+a_1x+a_2x^2+\cdots+a_nx^n,$$
where each $a_r$ is an integer, $r=0,1,2,\ldots,n$. Find the value of $n$ such that
$$a_0+a_2+a_3+a_4+\cdots+a_{n-2}+a_{n-1}=60-\frac{n(n+1)}2.$$
$$x+(1+x)^2+(1+x)^3+\cdots+(1+x)^n=a_0+a_1x+a_2x^2+\cdots+a_nx^n,$$
where each $a_r$ is an integer, $r=0,1,2,\ldots,n$. Find the value of $n$ such that
$$a_0+a_2+a_3+a_4+\cdots+a_{n-2}+a_{n-1}=60-\frac{n(n+1)}2.$$