A) \[\frac{n}{4n+6}\]
B) \[\frac{1}{6n+4}\]
C) \[\frac{n}{6n+4}\]
D) \[\frac{n}{3n+7}\]
Correct Answer: C
Solution :
Let \[{{S}_{n}}=\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{(3n-1)(3n+2)}\] \[=\frac{1}{3}\left[ \frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+....+\frac{1}{3n-1}-\frac{1}{3n+2} \right]\] \[=\frac{1}{3}\left[ \frac{1}{2}-\frac{1}{3n+2} \right]\] \[=\frac{n}{6n+4}\]
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