In this problem, you do NOT have to do formal proofs. Feel free to use phrases like, "We can see by inspection that sup A1 = 42." For each of the following sequences {am}, define the set A, = {ar : k...

n} and the numbers s, = sup An and in = inf An as in the definition of lim sup and lim inf given in Session 25. Give an explicit formula in terms of n for Sn and in. (Your formula may be piecewise-defined.) Determine lim sup an and lim inf an and use your results to determine whether {an} converges. (2) {"} (-1)* "/>
Extracted text: In this problem, you do NOT have to do formal proofs. Feel free to use phrases like, "We can see by inspection that sup A1 = 42." For each of the following sequences {am}, define the set A, = {ar : k > n} and the numbers s, = sup An and in = inf An as in the definition of lim sup and lim inf given in Session 25. Give an explicit formula in terms of n for Sn and in. (Your formula may be piecewise-defined.) Determine lim sup an and lim inf an and use your results to determine whether {an} converges. (2) {"} (-1)*