Verified Solution • 2025–26 Session moderate

QJEEM21Maa26e: JEE Main 2021 Mathematics - Class 12 JEEM21Maa26e Solution: lim x → 2 ⁡ ( ∑ n = 1 9 x n ( n + 1 ) x 2 + 2 ( 2 n + 1 ) x + 4 …

lim_{x \to 2} (\sum_{n = 1}^{9} \frac{x}{n (n + 1) x^{2} + 2 (2 n + 1) x + 4})

is equal to :

Multiple Choice Options

A 944
B 524
C 15
D 736

Step-by-Step Verified Solution

S = lim_{x \to 2} \sum_{n = 1}^{9} \frac{x}{n (n + 1) x^{2} + 2 (2 n + 1) x + 4}

S = \sum_{n = 1}^{9} \frac{2}{4 (n^{2} + 3 n + 2)} = \frac{1}{2} \sum_{n = 1}^{9} (\frac{1}{n + 1} - \frac{1}{n + 2})

S = \frac{1}{2} (\frac{1}{2} - \frac{1}{11}) = \frac{9}{44}

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