2^(n)(An^2+Bn+C)-4{2^(n-1)[A(n-1)^2+B(n-1)+C]}+4{2^(n-2)[A(n-2)^2+B(n-2)+C]} -(n+1)2^n = 0
You asked:
Investigate the equation: \({2}^{n} \left(A {n}^{2} + B n + C\right) - 4 \cdot {2}^{n - 1} \left({A\left( n - 1 \right)}^{2} + B\left( n - 1 \right) + C\right) + 4 \cdot {2}^{n - 2} \left({A\left( n - 2 \right)}^{2} + B\left( n - 2 \right) + C\right) - \left(n + 1\right) \cdot {2}^{n} = 0\).