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Sequences and Series

Sequences and Series. Factorials and Sequences. Factorials. Factorials are numbers that are found by using the products of consecutive numbers. What does that mean? 1 * 2 * 3 * 4 = 24 In factorial notation, this would be 4! Try one: 7! 5! 3! Now use the calculator. Press the number. (7)

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Sequences and Series

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  1. Sequences and Series Factorials and Sequences

  2. Factorials • Factorials are numbers that are found by using the products of consecutive numbers. • What does that mean? • 1 * 2 * 3 * 4 = 24 • In factorial notation, this would be 4! • Try one: • 7! 5! 3! • Now use the calculator. • Press the number. (7) • <Math>; Arrow over to PRB; Option 4 • <Enter> (5040)

  3. Factorials • Remember 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 • We can use this information to simplify. • = 336 • 6 * 7 * 8 • 336 • Try a couple. • 30 72 11880 Expand the factorial. Cancel out the numbers that are the same. Multiply what is left.

  4. Sequences • Sequence means to follow one thing after another in a certain order. • Same thing in math. • We need to know the notation of sequence in order to work with it. • = 2n – 1 is a sequence. • is the name of the sequence • 2n – 1 is the operation needed to satisfy the sequence. • Notice the “n”? It is the same number for both.

  5. Sequences • Find the first 4 terms of the sequence. • (That means n = 1; n = 2; n = 3; n = 4) • = 2n – 1 • = 2(1) – 1 • = 2 – 1 • = 1 • = 2(2) – 1 • = 4 – 1 • = 3 • = 2(3) – 1 • = 6 – 1 • = 5 • = 2(4) – 1 • = 8 – 1 • = 7 Plug each of the n values into the sequence and solve. (1, 3, 5, 7)

  6. Sequences • Try a harder one: • = • = • = • = (

  7. Sequences • Sometimes you only need to find one term. • You know which one based on the “n” value asked for. • , • =

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