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Determine whether the given sequence $\{a_n\}$ is convergent by deciding on monotonicity and boundness. Explain your answer.

$$\{a_n\}=\frac{n+1}{2n+1}$$

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Since you are new to this site, please consider reading this: How to ask a homework question? I wrote this comment because the question sounds homework-like. – Peter Tamaroff Sep 22 '12 at 20:50
Are you having trouble determining whether the sequence is monotonic? Determining whether the sequence is bounded? Showing that monotonic bounded sequences are convergent? What sort of trouble is it? – Trevor Wilson Sep 22 '12 at 22:28

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Your best bet is to express $$a_n = A + \dfrac{B}{2n+1}$$ In this way you can prove boundedness and monotonicity.

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And even the limit! – Brian M. Scott Sep 22 '12 at 20:55

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