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Pascal's triangle
- Lesson: 1a54:32
- Lesson: 1b10:52
- Lesson: 2a5:28
- Lesson: 2b1:03
- Lesson: 2c1:10
- Lesson: 2d10:06
- Lesson: 3a2:33
- Lesson: 3b6:26
Pascal's triangle
A Pascal's triangle is a number triangle of the binomial coefficients. The first row of the triangle is always 1.
Lessons
- 1.Expand:a)i) (a+b)0 =
ii) (a+b)1 =
iii) (a+b)2 =
iv) (a+b)3 =
Use Pascal's Triangle to expand:
i) (a+b)4 =
ii) (a+b)5 =b)Investigating Pascal's Triangle - 2.Pascal's Triangle - sum of numbers in each rowa)
Row Pattern Corresponding binomial expression Sum of the numbers in,the row Express the sum as a power of 2 1 1 (a+b)0 2 1 1 (a+b)1 3 1 2 1 (a+b)2 4 1 3 3 1 (a+b)3 5 1 4 6 4 1 (a+b)4 : : : : : n (a+b)n−1 n+1 (a+b)n b)What is the sum of the numbers in the 10th row of Pascal's Triangle?c)What is the sum of the coefficients in the expansion of (a+b)50 ?d)Express the number pattern of Pascal's triangle in "combination" form, then deduce the following formula:
nC0 + nC1 + nC2 + nC3 + … + nCn−2 + nCn−1 + nCn = 2n - 3.Without using a calculator, evaluate:a)10C0 + 10C1 + 10C2 + … + 10C9 + 10C10b)5C0 + 5C1 + 5C2 + 5C3 + 5C4
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Pascal's triangle
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