Series and Sequences - Mrs. Hall's Class- best deck

Question 1

Formula for nth term of arithmetic sequence

Answer 1

an=a1+(n-1)d

Question 2

formula for arithmetic series (sum of arithmetic sequence)

Answer 2

sn=n/2(a1+an)

Question 3

Common difference (definition and formula)

Answer 3

difference between terms in an arithmetic sequence.

a(sub n+1) - a(sub n)

Question 4

Formula for the nth term of a geometric sequence

Answer 4

an=a1r^(n-1)

Question 5

Common ration (definition and formula)

Answer 5

multiplication or division factor in a geometric sequence.

r=a(sub n)/a(sub n-1)

Question 6

formula for a basic (finite) geometric series

Answer 6

sn=a1(1-r^n)/(1-r)

Question 7

Formula for an infinite geometric series

Answer 7

sn=a1/(1-r)

Question 8

When is geometric series infinite?

Answer 8

When |r| < 1

Question 9

The limit of an infinite geometric series may or may not exist when?

Answer 9

when the nth term approaches 0.

Question 10

The limit of an infinite geometric series does not exist when?

Answer 10

When the nth term does not approach 0.

Question 11

To find the limit when the nth term of a sequence is given as an “ugly” fraction….

Answer 11

divide each term in the fraction by the highest power of n that appears in the fraction and then evaluate the fraction for n–>infinity

Question 12

A series is defined as convergent if…

Answer 12

it has a limit value

Question 13

a series is defined as divergent if…

Answer 13

it has no limit value

Question 14

divergent or convergent…infinite arithmetic series

Answer 14

divergent because it has no limit

Question 15

divergent or convergent…infinite geometric series, |r|>1

Answer 15

divergent because it has no limit

Question 16

divergent or convergent…infinite geometric series, |r|<1

Answer 16

convergent because it has a limit

Question 17

Ratio test for convergence

Answer 17

used for non arithmetic/geometric series of positive terms:
find ratio as n–>infinity of
a(sub n+1)/a(sub n)

if ratio > 1 it’s divergent
if ration =1 you have to use different test

Question 18

if ratio test for convergence gives you ratio=1

Answer 18

(only for series of positive terms)
compare all terms of the series to corresponding terms of a known series.
if all terms of unknown series < known series, then convergent;
if all terms of unknown series > known series then divergent

Question 19

is this special series divergent or convergent:

1+1/2+1/3+1/4+1/5+…+1/n

Answer 19

divergent

Question 20

sigma notation

Answer 20

starting term number on bottom, ending term on top, nth term formula to the right. Way to note series formula

Question 21

Binomial Expansion Formula

Answer 21

sigma (r=0, n) n!/(r!(n-r)!(x^n-r)y^r
or
sigma(r=o, n) nCr(x^n-r)y^r

Question 22

what does nCr stand for

Answer 22

n!/(r!(n-r)!)

Question 23

what does 0! equal?

Answer 23

1

Question 24

what is (x+y)³

Answer 24

x³+3x²y+3xy²+y³

Question 25

what is (x+y)⁴

Answer 25

x⁴+4x³y+6x²y²+4xy³+y⁴

Question 26

what are the 4 Binomial Theorem Facts

Answer 26

1. There are always n+1 terms in the expansion
2. The first term is always x^n; last term is always y^n
3. Moving left to right, the powers of x decrease and the powers of y increase.
4. The powers of x and y in each term always add up to n.