4.4 Binomial expansions
Lecture Outline
Brief History
Applications
Pascal’s triangle
Binomial expansions using Pascal’s triangle
Example 1
Your turn!
Binomial expansions using combinations
Combinations
Combinations
Combinations
Alternative formula for (_^n)C_r
Example 2
Computations of some nCr
Comparisons: Pascal’s triangle and Combinations
Binomial expansions using combinations
Example 3
Your turn!
Example 4
Solution
Your turn!
Solution
Binomial expansions when n is any rational number
Binomial expansions when n is any rational number
Formula for the Expansion of (1+x)^n
Why |x|<1?
What is the importance of the expansion when n is a negative or fraction?
Example 5
Solution (continued)
Your turn!
Solution
Expansion of (a+bx)^n
Example 6
Your turn!
Solution
Your turn!
Solution
Example 7
Solution
Learning outcomes
Formulae
Preview activity: Mathematics of Finance
2.21M
Категория: МатематикаМатематика
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4.4 Binomial expansions

1. 4.4 Binomial expansions

Foundation Year Program
NUFYP Mathematics
4.4 Binomial expansions
Joohee Hong
2019-2020

2. Lecture Outline

Foundation Year Program
Lecture Outline
Expansion of
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