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 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 S, and in. (Your formula may be piecewise-defined.) Determine lim sup a,n and lim inf a, and use your results to determine whether {an} converges. (b) {an}, where an = if n is odd and an = ; if n is even. | %3D "/>
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 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 S, and in. (Your formula may be piecewise-defined.) Determine lim sup a,n and lim inf a, and use your results to determine whether {an} converges. (b) {an}, where an = if n is odd and an = ; if n is even. | %3D