Sequences, Series, and Probability

Question 1

nPr

Answer 1

Permutation, order matters,

n!/(n-r)!

Question 2

nCr

Answer 2

Combination, order doesn’t matter, nPr/r! or n!/(n-r)!r!

Question 3

Binomial Theorem

Answer 3

nC0 a^n + nC1 a^n-1 b1 + … + nCn-1 a^1 b^n-1 + nCn b^n

Question 4

Sequence

Answer 4

List of #s with a certain pattern, finite or infinite, can converge or diverge

Question 5

Series

Answer 5

Sum of the terms of a sequence, finite or infinite

Question 6

Arithmetic Sequence

Answer 6

A sequence with a common difference between terms

Question 7

Arithmetic RF

Answer 7

an = an-1 + d

Question 8

Arithmetic EF

Answer 8

an = a1 + d(n-1)

Question 9

Arithmetic Series Formula

Answer 9

Sn = n/2(a1 + an)

Question 10

Geometric Sequence

Answer 10

A sequence with a common ratio between terms

Question 11

Geometric EF

Answer 11

an = a1 • (r)^(n-1)

Question 12

Geometric RF

Answer 12

an = r(an-1)

Question 13

Sigma (Summation) Notation

Answer 13

n of last term
——————
\
  \
    \   Formula in
    /   terms of n
  /
/
——————
n of first value

Question 14

Partial Sum of Geometric Series

Answer 14

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

Question 15

Converging Geometric Series

When does it converge?

Answer 15

A series will only converge if |r| < 1

S = a1/1-r