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 {an}, define the set A, = {ar : k...

n} and the numbers s, = sup A, and i, = 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 a, and lim inf a, and use your results to determine whether {an} converges. {sin ("=)}) (n-1)A (c) {0, 1,0, –1,0, 1,0, –1,..} (Note that this is the sequence "/>
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 {an}, define the set A, = {ar : k > n} and the numbers s, = sup A, and i, = 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 a, and lim inf a, and use your results to determine whether {an} converges. {sin ("=)}) (n-1)A (c) {0, 1,0, –1,0, 1,0, –1,..} (Note that this is the sequence