Solve the recurrence relation. Need some help x(n)= x(n-1) + 2*n + 3 ; Given x(0)=4;
I'm using backwards substitution
x(n-1)= [x(n-2) + 2(n-1) + 3] + 2*n+ 3
x(n-2)= [x(n-3) + 2(n-2) + 3] + x(n-2) + 2(n-1) + 3 + 2*n + 3 so on and so forth......
so i write the general expression as :
x(n) = x(n-i) + [something here] + i*3
but i am not sure because i'm getting terms like 2(n-3) + 2(n-2) + 2(n-1)+ 2(n) ...
do i write these terms as (2-i-1) ?
any help will be appreciated

make for your series the Ansatz $$x_n=A+Bn+Cn^2$$
