QJEEM19Ma6c03: JEE Main 2019 Mathematics - Class 12 JEEM19Ma6c03 Solution: If α and β are the roots of the equation 375x 2 – 25x – 2 = 0,…

Question

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If

α

and

β

are the roots of the equation 375x² – 25x – 2 = 0, then

lim_{n \to \infty} \sum_{r = 1}^{n} α^{r} + lim_{n \to \infty} \sum_{r = 1}^{n} β^{r}

is equal to :

Accepted Answer

α

and

β

are the two root of 375x² - 25x - 2 = 0

Both of the roots are lie in (-1, 1) hence sum of given series is finite

lim_{n \to \infty} (\frac{α}{1 - α} + \frac{β}{1 - β}) = \frac{α (1 - β) + β (1 - α)}{(1 - α) (1 - β)}

\Rightarrow \frac{(α + β) - 2 α β}{1 - (α + β) + α β} = \frac{25 - 2 (- 2)}{375 - 25 - 2} = \frac{29}{348}

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