Expansion of (1 + x)^n, Pascal’s triangle (HSC SSCE Mathematics Extension 1): Flashcards
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What does the Binomial Theorem describe?
What does the Binomial Theorem describe?
It describes expanding expressions like (1 + x)^n.
What is Pascal's Triangle?
What is Pascal's Triangle?
A triangle of numbers where each number sums the two above.
What is the formula for (1 + x)^n?
What is the formula for (1 + x)^n?
It's (1 + x)^n = ∑(n choose r) x^r from r=0 to n.
What does (n choose r) represent?
What does (n choose r) represent?
It represents ways to choose r items from n.
What is the first row of Pascal's Triangle?
What is the first row of Pascal's Triangle?
The first row is 1.
How do you construct Pascal's Triangle?
How do you construct Pascal's Triangle?
Each number is the sum of the two numbers above it.
What is a property of every row in Pascal's Triangle?
What is a property of every row in Pascal's Triangle?
Every row starts and ends with 1.
What does the sum of coefficients in row n equal?
What does the sum of coefficients in row n equal?
It equals 2^n.
How can Pascal's Triangle help in expansions?
How can Pascal's Triangle help in expansions?
It provides coefficients for binomial expansions.
What is Pascal's identity?
What is Pascal's identity?
It's (n choose r) = (n-1 choose r-1) + (n-1 choose r).