Sequences

Question 1

decreasing sequence

Answer 1

an+1 < an for every n

Question 2

increasing sequence

Answer 2

an+1 > an for every n

Question 3

monotonic series

Answer 3

either a decreasing or increasing sequence

Question 4

lower bound

Answer 4

there exists a number n in such that an >= m for every n

Question 5

upper bound

Answer 5

there exists a number M such that an <= M for every n

Question 6

bounded sequence

Answer 6

sequence is bounded below & above

Question 7

find the constant of the arithmetic sequence

Answer 7

an+1 - an

Question 8

find the constant of the geometric sequence

Answer 8

an+1/an

Question 9

what are the 4 limit rules

Answer 9

1. lim(an +bn) = lim(an) + lim(bn)
2. lim(can) = clim(an) where c = constant
3. lim(an.bn) = lim(an) . lim(bn)
4. lim(an/bn) = lim(an)/lim(bn)

Question 10

what are the 2 types of divergences

Answer 10

1. oscillates
2. go to infinity

Question 11

what is big O

Answer 11

denotes a class of functions for which lim(fn/(n^k) = C where C is a non-zero constant