If α and β are the roots of the equation 375 x 2 - 25 x - 2 = 0 , then l i m n → ∞ ∑ r = 1 n α r + l i m n → ∞ ∑ r = 1 n β r is equal to:

Step-by-step solution

For given quadratic 375 x 2 - 25 x - 2 = 0 , its roots are, α , β = 25 ± 25 2 + 2 × 4 × 375 2 × 375 ⇒ α < 1 , β < 1 Also, α + β = 25 375 ,   α β = - 2 375 Now l i m n → ∞ ∑ r = 1 n α r + l i m n → ∞ ∑ r = 1 n β r = α 1 - α + β 1 - β a + a r + a r 2 + . . . . .   infinite    terms = a 1 - r        if     r < 1 = &#94