A) \[\frac{n}{6n-4}\]
B) \[\frac{n}{6n+3}\]
C) \[\frac{n}{6n+4}\]
D) \[\frac{n+1}{6n+4}\]
Correct Answer: C
Solution :
Given, \[\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...\] \[+\frac{1}{(3n-1)(3n+2)}\] \[=\frac{1}{3}\left[ \left( \frac{1}{2}-\frac{1}{5} \right)+\left( \frac{1}{5}-\frac{1}{8} \right)+\left( \frac{1}{8}-\frac{1}{11} \right) \right.\] \[\left. +...+\left( \frac{1}{3n-1}-\frac{1}{3n+2} \right) \right]\] \[=\frac{1}{3}\left[ \frac{1}{2}-\frac{1}{3n+2} \right]\] \[=\frac{3n+2-2}{6(3n+2)}=\frac{n}{6n+4}\]
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