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Pascal's triangle

any number is sum of the two numbers immediately above it

nCr

number combindations of n items taken r at a time

n

total number

R

number taken

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

(n above r)

n!

n*(n-1)*(n-2)*(n-3) etc.

nCr GDC

menu > probability > combination

rules of binomial expansion (a+b)^n

there are exponent n + 1 terms

! (2x)^3 =

2^3*x^3 = 8x^3

! when a or b negative

odd exponent will still result in negative number

constant term

numerical value without variable

find constant term

use information known and write general formula

n

(n over 1) coefficient

if you know r but not n and coefficient

graph nCr(x, r) r has to be specific value and look at table. y will be coefficient you know and x = n

number of terms

exponent + 1

n

total number of items

R

number of items taken

nCr(n, r)

find number of combinations on GDR

find number of combinations

n! as many numbers as r from high to low / r!

binomial expansion formula

use combination formula or GDC to find coefficient

always 1

coefficient of first term

always n

coefficient of second term

find term with given power

- write general formula with information given (n is given)

if a or b is negative

write (-1) in brackets separately so you get sign right

if a or b is for example 2x

easier to write (2) and then (x) separately

it is *r=4*

when you want the fifth term

- write general formula

when you want constant term

when you know r but not n

- make a graph with nCr(x, known r)

top # - bottom # + 1

Value of Series: Add the given term next to Σ for number of times that is determined by

n*(n-1)*(n-2)...1

n! =

(n+3)*(n+2)*(n+1)*n!

(n+3)! =

n! / (k!(n-k)!)

C(n,k) = nCk = Cn,k =

The first term would be positive and alternate from there

For expanding binomials, if the first nomial is positive but second nomial is negative

(C(c,c-d))*(a^d)*(b^(c-d))

Specific Term Problem Guide: (a+b)^c, term containing a^d

(C(c,c/2))*(a^d)*(b^(c/2))

Specific Term Problem Guide: (a+b)^c, middle term

c+1

How many terms will there be in the following expansion? (a+b)^c

Addition

to join two or more quantities

term

An element or number in a sequence.

a

Value of row a in position a-1 and 2 is

Even

An integer n is defined to be even if n=2k for some integer k.