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3. If row 3 in Pascal's triangle is 1, 3, 3, 1, what is row 2 in Pascal's Triangle? 4. If row 8 in Pascal's triangle is 1, 8, 28, 56, 70, 56, 28, 8, 1, what is row 7 in Pascal's Triangle?

3. If row 3 in Pascal's triangle is 1, 3, 3, 1, what is row 2 in Pascal's Triangle? 4. If row 8 in Pascal's triangle is 1, 8, 28, 56, 70, 56, 28, 8, 1, what is row 7 in Pascal's Triangle?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Question 3:** If row 3 in Pascal’s triangle is 1, 3, 3, 1, what is row 2 in Pascal’s Triangle? --- **Question 4:** If row 8 in Pascal’s triangle is 1, 8, 28, 56, 70, 56, 28, 8, 1, what is row 7 in Pascal’s Triangle? --- **Explanation:** Pascal’s Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it. The rows start from row 0 at the top which is “1”. - For Question 3: - Row 3 is given as 1, 3, 3, 1. - Therefore, row 2 is 1, 2, 1, which are the coefficients of \((x + y)^2\). - For Question 4: - Row 8 is given as 1, 8, 28, 56, 70, 56, 28, 8, 1. - Therefore, row 7 is 1, 7, 21, 35, 35, 21, 7, 1, which are the coefficients of \((x + y)^7\). Understanding Pascal’s Triangle can greatly aid in combinatorics and algebra through concepts like binomial expansions.
Transcribed Image Text:**Question 3:** If row 3 in Pascal’s triangle is 1, 3, 3, 1, what is row 2 in Pascal’s Triangle? --- **Question 4:** If row 8 in Pascal’s triangle is 1, 8, 28, 56, 70, 56, 28, 8, 1, what is row 7 in Pascal’s Triangle? --- **Explanation:** Pascal’s Triangle is a triangular array of the binomial coefficients. Each number is the sum of the two directly above it. The rows start from row 0 at the top which is “1”. - For Question 3: - Row 3 is given as 1, 3, 3, 1. - Therefore, row 2 is 1, 2, 1, which are the coefficients of \((x + y)^2\). - For Question 4: - Row 8 is given as 1, 8, 28, 56, 70, 56, 28, 8, 1. - Therefore, row 7 is 1, 7, 21, 35, 35, 21, 7, 1, which are the coefficients of \((x + y)^7\). Understanding Pascal’s Triangle can greatly aid in combinatorics and algebra through concepts like binomial expansions.
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