1 / 8

Calculate

Calculate. 4C0, 4C1, 4C2, 4C3 and 4C4 4C0=1, 4C1=4, 4C2=6, 4C3=4 and 4C4=1 Where have you seen this sequence of numbers before?. Pascal’s Triangle Revisited. 0C0 1C0 1C1 2C0 2C1 2C2 3C0 3C1 3C2 3C3 4C0 4C1 4C2 4C3 4C4 n th line nC0 nC1 nC2 etc… (starts on the 0 th line).

falala
Download Presentation

Calculate

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculate • 4C0, 4C1, 4C2, 4C3 and 4C4 • 4C0=1, 4C1=4, 4C2=6, 4C3=4 and 4C4=1 • Where have you seen this sequence of numbers before?

  2. Pascal’s Triangle Revisited • 0C0 • 1C0 1C1 • 2C0 2C1 2C2 • 3C0 3C1 3C2 3C3 • 4C0 4C1 4C2 4C3 4C4 • nth line nC0 nC1 nC2 etc… • (starts on the 0th line)

  3. Implication: Pascal’s Formula 0C0 1C0 1C1 2C0 2C1 2C2 3C0 3C1 3C2 3C3 4C0 4C1 4C2 4C3 4C4 Notice that each entry is equal to the sum of 2 entries from a proceeding row. For example: 4C2=3C1 + 3C2 This is known as Pascal’s Formula: nCr=n-1Cr-1 + n-1Cr

  4. Binomial Theorem Do you see a pattern in the coefficients?

  5. Pascal’s Triangle • 1 • 1 1 • 2 1 • 1 3 3 1 • 1 4 6 4 1 • 1 5 10 10 5 1 • 1 6 15 20 15 6 1 • nth line nC0 nC1 nC2 etc… • (starts on the 0th line)

  6. Example: Expand (x+y)6 • Try it yourself, use row 6 from Pascal’s Triangle (the seventh row counting from the top) or 6C0, 6C1 … 6C6 as the coefficients.

  7. Another Example HINT: expand (a+b)4 then sub in 2x for a and 1/y for b.

  8. Practice • Page 293 • Questions 1 to 12

More Related