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JEE Main20202 Sep 2020Morning ShiftMathematicsLimitsActual

If lim x → 1 x + x 2 + x 3 + . . . + x n - n x - 1 = 820 , n ∈ N then the value of n is equal to....

Correct answer

0

Step-by-step solution

lim x → 1 x + x 2 + x 3 + … . + x n - n x - 1 = 820                   0 0 form Applying L'Hospital rule lim x → 1 1 + 2 x + 3 x 2 + … . . + n x n - 1 1 = 820 ⇒ 1 + 2 + 3 + … … + n = 820 ⇒ n ( n + 1 ) 2 = 820 ⇒ n 2 + n = 1640 ⇒ n 2 + n - 1640 = 0 ⇒ n = 40 ,   - 41 Since n is natural number ⇒ n = 40 .

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