$\alpha$ & $\beta\;$are +ve roots of $\;x^2-2ax+ab=0\;$ then for $\;n \in N\;$$(0 \lt b \lt a)\;S_{n}=1+2(\large\frac{b}{a})$$+3(\large\frac{b}{a})^{\normalsize 2}$$+\;...+\;n$$(\large\frac{b}{a})^{n-1}\;$ can not exceed .

Question

$(a)\;\frac{\alpha}{\beta}\qquad(b)\;\frac{\beta}{\alpha}\qquad(c)\;|$$\large\frac{\alpha+\beta}{\alpha-\beta}|$$\qquad(d)\;(\large\frac{\alpha+\beta}{\alpha+\beta})^{4}$