AMC 12 Sequences, Series & Limits Flashcards
6 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 AMC 12 Sequences, Series & Limits flashcards as text
What is lim(x→∞) of (3x² + 1)/(x² − 2)?
Answer: 3
Dividing numerator and denominator by x² yields (3 + 1/x²)/(1 − 2/x²) → 3 as x → ∞.
What is the sum 1/(1·2) + 1/(2·3) + 1/(3·4) + … + 1/(n(n+1))?
Answer: n/(n+1)
Partial fractions give 1/(k(k+1)) = 1/k − 1/(k+1), and the series telescopes to 1 − 1/(n+1) = n/(n+1).
The Fibonacci sequence is defined by F₁ = 1, F₂ = 1, Fₙ = Fₙ₋₁ + Fₙ₋₂. What is F₇?
Answer: 13
Computing in order: F₃=2, F₄=3, F₅=5, F₆=8, F₇=13.
What is lim(x→0) of sin(x)/x?
Answer: 1
This is a standard fundamental limit: lim(x→0) sin(x)/x = 1.
An arithmetic series has 10 terms with first term 1 and total sum 100. What is the common difference?
Answer: 2
S = n/2·(2a₁ + (n−1)d) gives 100 = 5(2 + 9d), so 9d = 18 and d = 2.
Which formula gives the sum of the first n perfect squares?
Answer: n(n+1)(2n+1)/6
The sum 1² + 2² + … + n² = n(n+1)(2n+1)/6.
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