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Pre-Calculus 11 · Unit 1
Sequences & Series.
1.1 · Arithmetic Sequences
Arithmetic Sequences.
The staircase that climbs by the same step every time. Derive tₙ = t₁ + (n−1)d and leap to any term.
1.2 · Arithmetic Series
Arithmetic Series.
Add a staircase fast. Gauss-pair the terms and prove Sₙ = n/2 (t₁ + tₙ).
1.3 · Geometric Sequences
Geometric Sequences.
Multiply instead of add. The common ratio r and tₙ = t₁ · rⁿ⁻¹.
1.4 · Geometric Series
Geometric Series.
Sum a multiplying chain with the shift-and-subtract trick: Sₙ = t₁(rⁿ − 1)/(r − 1).
1.5 · Infinite Geometric Series
Infinite Series.
When |r| < 1, infinitely many terms add to a finite number: S = t₁/(1 − r).
Math 10
Made by
Lina Ahmadi
“Curiosity is the limit.”