1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i)...
1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i) For each sequence, give its lim
sup and its lim inf. Show your reasoning; definitions are not
required.(ii) For each sequence, determine its set of subsequential
limits. Proofs are not required.
Q1. City K's home phone numbers have 6 digits. In a home phone
number, each digit...
Q1. City K's home phone numbers have 6 digits. In a home phone
number, each digit can be any number of 0,1,..., 9, except that a
phone number many not start with the following sequences: a)
reserved for emegency services: 110, 119, 120, 120. b) reserved for
domestic and international dial prefixes: 0. At most how many
distinct home phones can this system accommoodate? For Example
120193 and 018483 are invalid.
Q2. In how many ways can we assign n...
Consider the following numbers 3, 6, 9, 12, . . . , 75. Show
that if...
Consider the following numbers 3, 6, 9, 12, . . . , 75. Show
that if we pick 15 arbitrary numbers from them, then we will find
two that have sum equal to 81. I understand that there are 12
distinct sets containing pairs that sum to 81 plus a singleton
subset {3}. but wouldn't this mean that there are 2 remaining
"empty holes" that need to be filled? Not sure how to apply the
pigeonhole principle here.