Question: Consider the sequence an=4n1-n2 for n2.To determine whether {an} is increasing or decreasing, we consider the behavior of the function f satisfying f(n)=an for all

Consider the sequence an=4n1-n2 for n2.To determine whether {an} is increasing or decreasing, we consider the behavior of the function f satisfying f(n)=an for all n.f is on the interval , thefore {an} is also and is therefore monotonic.The sequence is bounded above by , and bounded below by We can conclude that the sequnce is convergent because it is monotonic and bounded.

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