If α and β are the roots of the equation 375x2−25x−2=0 then Limn→∞∑r=1nαr+Limn→∞∑r=1nβr=λμ then find λ+μ=_________(λ,μ are coprime)

Given α1−α+β1−β=29348⇒λ=29, μ=348 ⇒λ+μ=377

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If $α$ and $β$ are the roots of the equation $375 x^{2} - 25 x - 2 = 0$ then $\underset{n \to \infty}{L i m} \sum_{r = 1}^{n} α^{r} + \underset{n \to \infty}{L i m} \sum_{r = 1}^{n} β^{r} = \frac{λ}{μ}$ then find $λ + μ =$ _________( $λ, μ$ are coprime)

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answer is 377.

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Given $\frac{α}{1 - α} + \frac{β}{1 - β} = \frac{29}{348}$

$\Rightarrow λ = 29, μ = 348 \Rightarrow λ + μ = 377$

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