If α and β are the roots of the equation 375x2 - 25x - 2 = 0, then displaystyle limn →∞ ∑nr=1 αr + limn→∞ ∑nr=1 βr is equal to :

Question

If α and β are the roots of the equation 375x2 - 25x - 2 = 0, then displaystyle limn →∞ ∑nr=1 αr + limn→∞ ∑nr=1 βr is equal to : (A) (21/346) (B) (29/358) (C) (1/12) (D) (7/116)

Tardigrade Admin · Accepted Answer

375x2 -25x-2=0 α + β = (25/375), αβ = (-2/375) ⇒ (α + α2 + ..... textupto textinfinite textterms) + (β +β2 + .... textupto textinfinite textterms) = (α/1-α) + (β/1-β) = (1/12)

Q. If $α$ and $β$ are the roots of the equation $375 x^{2} - 25 x - 2 = 0$ , then $n \to \infty lim r = 1 \sum n α^{r} + n \to \infty lim r = 1 \sum n β^{r}$ is equal to :

$\frac{21}{346}$

$\frac{29}{358}$

$\frac{1}{12}$

$\frac{7}{116}$

$375 x^{2} - 25 x - 2 = 0$
$α + β = \frac{25}{375}, α β = \frac{- 2}{375}$
$\Rightarrow (α + α^{2} + ..... upto infinite terms) + (β + β^{2} + .... upto infinite terms)$
$= \frac{α}{1 - α} + \frac{β}{1 - β} = \frac{1}{12}$

Q. If α and β are the roots of the equation 375x2−25x−2=0, then n→∞lim​r=1∑n​αr+n→∞lim​r=1∑n​βr is equal to :

34621​

35829​

121​

1167​