Question: Consider the sequence an=2n1-n2 for n2To determine whether {an} is increasing or decreasing, we consider the behavior of the function f satistying f(n)=an for all

Consider the sequence an=2n1-n2 for n2To determine whether {an} is increasing or decreasing, we consider the behavior of the function f satistying 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 byWe can conclude that the sequace is coervergent because it is monotonic and bounded.

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