Chapter 8 The Binomial Expansion Flashcards
1
Q
How is Pascal’s triangle formed?
A
By adding adjacent pairs of numbers to find the numbers on the next row
2
Q
What does the (n+1)th row of Pascal’s triangle give the coefficients for?
A
The expansion of (a+b)^n
3
Q
How can you find entries in Pascal’s triangle quickly?
A
Use the nCr button on the calculator
4
Q
What is the formula for nCr?
A
n! / r!(n-r)!
5
Q
How do you find the rth entry in the nth row of Pascal’s triangle?
A
(n-1)C(r-1)
6
Q
What is the binomial expansion of (a+b)^n?
A
a^n + nC1 x a^n-1 x b + nC2 x a^n-2 x b^2 + … + b^n
7
Q
What is the general term in the expansion of (a+b)^n?
A
nCr x a^n-r x b^r
8
Q
How do you find an approximation for a binomial expansion?
A
Ignore larger powers of x
9
Q
When can you find an approximation for a binomial expansion?
A
When the value of x is less than 1
