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JEE Main202126 Aug 2021Evening ShiftMathematicsLimitsActual

lim x → 2 ∑ n = 1 9 x n ( n + 1 ) x 2 + 2 ( 2 n + 1 ) x + 4 is equal to :

Options

  1. A5 24
  2. B7 36
  3. C1 5
  4. D9 44

Correct answer

D. 9 44

Step-by-step solution

lim x → 2     ∑ n = 1 9 x n ( n + 1 ) x 2 + 2 ( 2 n + 1 ) x + 4 lim x → 2 ∑     n = 1 9 x n n + 1 x 2 + 2 n x + 2 n + 1 x + 4 lim x → 2 ∑     n = 1 9 ( n + 1 ) x + 2 - n x + 2 ( n + 1 ) x + 2 n x + 2 lim x → 2 ∑     n = 1 9 1 ( n x + 2 ) - 1 ( n + 1 ) x + 2 = 1 x + 2 - 1 2 x + 2 1 2 x + 2 - 1 3 x + 2 . . . . + 1 9 x + 2 - 1 10 x + 2 1 x + 2 - 1 10 x + 2 ⇒    lim x → 2 1 x + 2 - 1 10 x + 2 = 9 44 ⇒ &#1

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