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

asked by guest
on Jan 16, 2025 at 2:42 am



You asked:

Investigate the equation: 2n(An2+Bn+C)−4⋅2n−1(A(n−1)2+B(n−1)+C)+4⋅2n−2(A(n−2)2+B(n−2)+C)−(n+1)⋅2n=0{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.

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