If $3 x=1+\frac{5}{8}+\frac{5}{8} \cdot \frac{9}{13}+\frac{5}{16}+\ldots$, then $x^4+4 x^3+6 x^2+4 x=$

If $\alpha, \beta, \gamma$ are the roots of the equation $3 x^3-26 x^2+52 x-24=0$ such that $\alpha, \beta, \gamma$ are in geometric progression and $\alpha<\beta<\gamma$, then $3 \alpha+2 \beta+\gamma=$

Let $f(n)=A(-2)^n+B(-3)^n \forall A, B \in \mathbf{R}$ and $n \in \mathbf{N}-\{1,2\}$. If $f(n)+a f(n-1)+b f(n-2)=0$, then $(a+b)(b-a)=$