i have tried to replace the value of n which isKeeping in mind that this is not the Free Math Answers forum, but Free Math Help. So, where do you need help?
In particular, what are you supposed to deduce this from? What have you learned that might be of use? What did you try?
As n tends to infinity, 1/(2n+1)^3 tends to 0 and also 1/(2n+1)^3 is a decreasing sequence. Therefore it converges.Also, this is the series \(\large{ \sum\limits_{n = 0}^\infty {\frac{{{{( - 1)}^n}}}{{{{(2n + 1)}^3}}}}} \)
Can you show that the series does converge? If so please post.