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JEE Mains · Maths · STD 11 - 12. limits
\(\lim _{x \rightarrow 2}\left(\sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}\right)\) is equal to :
- A \(\frac{9}{44}\)
- B \(\frac{5}{24}\)
- C \(\frac{1}{5}\)
- D \(\frac{7}{36}\)
Answer & Solution
Correct Answer
(A) \(\frac{9}{44}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}=\lim _{x \rightarrow 2} \sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}\) \(S=\sum_{n=1}^{9} \frac{2}{4\left(n^{2}+3 n+2\right)}=\frac{1}{2} \sum_{n=1}^{9}\left(\frac{1}{n+1}-\frac{1}{n+2}\right)\)…
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