2 - chapter 4 - sequences and series

Question 1

term to term rule vs position to position rule

Answer 1

un+1 = un+ a
un = an +b

Question 2

increasing, decreasing periodic sequence

Answer 2

increasing - un+1 > un
decreasing un+1 < un
periodic - terms start repeating after a while un+k = un

Question 3

limit of a sequence

Answer 3

converges - gets closer and closer to a certain value
diverges - terms increase with no limit

Question 4

to find the limit of a convergent sequence

Answer 4

set un+1 = un = L and solve for L

Question 5

series

Answer 5

sum of a sequence to a point
Sn = u1 + u2 + …. + un
= Σ u r
from r = 1 to r = n

Question 6

arithmetic seuqence

Answer 6

have a common difference between each term
un = a+ (n-1)d

Question 7

arithmetic series

Answer 7

Sn = n/2 (2a + (n-1)d)
= n/2 (a+L)
where L = un = a+ (n-1)d

Question 8

geometric sequence

Answer 8

has a common ratio
un = ar ^n-1

Question 9

geometric series

Answer 9

Sn = a(1-r^n)/1-r when r<1
or = a(r^n-1)/r-1 when r>1

Question 10

infinite geometric series

Answer 10

S∞ = a/1-r (if |r|<1)
if |r| >1 then the series diverges (sum is infinite)