Determine whether the sequence an=1n2is convergent. Justify your answer.Consider the sequence an=2n+1n+4. Find its limitasn.Let an=n2n2+1.(a)Is this sequence increasing, decreasing, or neither?(b)Isit bounded?(c) Does it converge? Ifso, what?Explain why a sequence can be bounded but not convergent. Provide an example.Suppose an=1+(-1)nn.(a)Is this sequence monotonic?(b)Isit bounded?(c) Does it converge? Explain your reasoning.Use the Squeeze Theorem to show thatan=sin(n)n0asn