lim _{x rightarrow 2}left(sum_{n=1}^{9} frac{ | vedclass

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Question

(A) माना $S = \lim _{x \rightarrow 2} \sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}$.$x = 2$ रखने पर:$S = \sum_{n=1}^{9} \frac{2}{4n^2 + 12n + 8}

Vedclass · Accepted Answer

$\frac{9}{44}$

Vedclass · Answer

(A) माना $S = \lim _{x \rightarrow 2} \sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}$.$x = 2$ रखने पर:$S = \sum_{n=1}^{9} \frac{2}{4n^2 + 12n + 8} = \sum_{n=1}^{9} \frac{1}{2(n+1)(n+2)}$आंशिक भिन्न का उपयोग करने पर:$S = \frac{1}{2} \sum_{n=1}^{9} \left( \frac{1}{n+1} - \frac{1}{n+2} \right)$यह एक टेलीस्कोपिंग श्रेणी है:$S = \frac{1}{2} \left( \frac{1}{2} - \frac{1}{11} \right) = \frac{9}{44}$.

$\lim _{x \rightarrow 2}\left(\sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}\right)$ का मान ज्ञात कीजिए :

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