Let {an} be a bounded sequence of numbers in r. we define a new sequence bn} as follows sup{an n n} = 1. prove that {by} is monotone. definition. if {an} is a bounded sequence in r, then the limsup, denoted lim sup an, is defined as: n oo lim sup an n > n} lim sup an (1) noo n oo 2. prove that the limit in (1) exists. 3. based on the definition of the lim sup above, what would the definition of lim inf be? 4. using the definition you gave in the previous problem, show that for bounded sequences, the lim inf always exists 5. prove that if lm sup{an} lim inffan} l. then the limit of {an} exists and equals l

First, think of what you know. you know that the number t the end of the equation will need to be subtracted because it is the money he lost from buying the lawn mower. and your first two weeks have negative profit, so that tells you that c and d are wrong. now you can plug any of the weeks into a and b to see which one works. i'll start with plugging week 1 into a.this isn't right because it says your answer for week one should be -90.so now we need to try the same thing with b.this one got you the right answer, (sometimes if you only check with one of the weeks multiple will work so you need to check with more of the weeks, but it worked out fine here)this means that b is the correct answer.let me know if you need more clarification. i hope this : )