7.1 Introduction and Pascal's Triangle

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Solved Examples

  1. The row for index 4 is: 1, 4, 6, 4, 1.
  2. Generate row for index 5 by adding adjacent terms:
    • Ends are always 1.
    • 1+4=51+4=5
    • 4+6=104+6=10
    • 6+4=106+4=10
    • 4+1=54+1=5
  3. Coefficients: 1, 5, 10, 10, 5, 1.
  4. Powers: aa decreases from 5 to 0; bb increases from 0 to 5.
  5. Expansion: a5+5a4b+10a3b2+10a2b3+5ab4+b5a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5.

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